







f(x + 2) 
20190226 

From a student: How do you use f(x) = 3x+1 to determine the transformed function of f(x + 2)? Answered by Penny Nom. 





Composition of functions 
20190224 

From Joshua: Let g(x)=(x)^(2)+x1
Find such a function f such that
(fog)(x)=(x)^(4)+2(x)^(3)3(x)^(2)4x+6 Answered by p. 





Function notation 
20190210 

From Paige: What is the difference between f(x+2) and f(x)+2? Answered by Penny Nom. 





y=lnx+(1+ln2)/2 and y=x^2 
20190128 

From Mike: Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.
The course is about logarithm and root functions... how should I solve this problem? Answered by Penny Nom. 





y = f(x) 
20181230 

From yogita: What is the actual meaning of "f(x)" ? Please give me full explanation Answered by Penny Nom. 





y = x  1 
20181130 

From alexis: what does this mean y=x1 Answered by Penny Nom. 





f(x) and f(x) 
20181019 

From Simran: what is difference between f(x) compared to f(x) on graph Answered by Penny Nom. 





The domain of f(g(x)) 
20180618 

From Joshua: What are the restrictions of the domain of f(g(x))? Answered by Penny Nom. 





Positive and negative values of a function 
20180130 

From Grayson: f(x)=x^6x^4
Interval: ( negative infinity, negative one )
Test Value: negative two
Function Value f(x): positive forty eight
Interval: ( negative one, zero )
Test Value: negative one
Function Value f(x): zero
Interval: ( zero, positive one )
Test Value: positive one
Function Value f(x): zero
Interval: ( positive one, positive infinity )
Test Value: positive two
Function Value f(x): positive forty eight
What is the sign of f(x) for each Interval? Answered by Penny Nom. 





f(x)=x^26x find f(x2) 
20171027 

From Kenneth: f(x)=x^26x find f(x2) Answered by Penny Nom. 





y = g(x + 1) 
20170627 

From Shamsudiin: HI there i am currently doing a level maths AS
I don't understand how to graph this Question y=g(x+1) i really need help please
please respond to this problem Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





The inverse of y=x^2+x+c 
20161221 

From Sam: What is the inverse of y=x^2+x+c for x? Answered by Penny Nom. 





The inverse of y = x(x  2) 
20161221 

From Sasha: Hello, I recently stumbled upon this question and I haven't been able to figure it out.
Why is the inverse of y=x(x2) not a function?
Suggest a domain restriction which would ensure that the inverse is a function.
Thank You :) Answered by Penny Nom. 





The derivative of the inverse of a function 
20161028 

From Kate: Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^1(4) if f(3)=4 and f'(3)=1/7 Answered by Penny Nom. 





A linear relationship 
20161016 

From Bianca: x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it? Answered by Penny Nom. 





The temperature inside and outside a greenhouse 
20160722 

From Mehzad: Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?
a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same Answered by Penny Nom. 





The composition of a function with itself 
20160717 

From Mel: If f(1 + 3x) = 1 * x, solve f(f(x)) Answered by Penny Nom. 





find f+g 
20160626 

From yzabelle: find f+g
f(x)=x^21
g(x)=square root of x+2 Answered by Penny Nom. 





sin 2x  sin x = 0 
20160424 

From lilly: sin 2x  sin x = 0 0 Answered by Penny Nom. 





The inverse function for f(x)=2x^2+5x 
20160423 

From Ashini: The inverse function for f(x)=2x^2+5x Answered by Penny Nom. 





The inverse of a function 
20160320 

From Billy: f(x) = Square root(x^2 + 2x)
What is the inverse? Answered by Penny Nom. 





The domain and range of a function 
20160219 

From Genius: State the domain and range
g(x)=x(x1) Answered by Penny Nom. 





The range of a function with a finite domain 
20160125 

From Hannah: Solve y=(1⁄4)x1 if the domain is (4,2,0,2,4).
I don't get how to do this. Can anyone help? Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





The range of a function defined piecewise 
20160113 

From sarah:
f(x)={x2, x<2
{x^24, 2_<x_<2
{x+2, x>2
find the range Answered by Penny Nom. 





The range of f(x)=(2x+2)/(x1) 
20151125 

From Nazrul: f : R to R is a function which is defined by f(x)=(2x+2)/(x1).
Is f(x) an onto function? Please explain.
What is the range of this function?
Thank you very much for your previous help. Answered by Harley Weston. 





Fencing around a rectangular field 
20151111 

From Darlene: Question from Darlene, a parent:
A farmer has 10,000 meters of fencing to use to create a rectangular field. He
plans on using some of the fencing to divide the rectangular field into two
plots of land by constructing a fence inside the rectangle that is parallel to one
of the sides. Let X be the width of the rectangular field. Write an equation
to express the area of the field as a function of X. Find the value of X that
maximizes the area of the field. Answered by Penny Nom. 





The domain of cos2x/(sinx2) 
20151102 

From Ameen: Find the domain of:
f(x) = cos2x/(sinx2) Answered by Penny Nom. 





y=f(x) and y=3/2f(x) 
20150527 

From Kevin: Could you please show me what change y=f(x) to y=3/2f(x) has gone through and please graph.
y=f(x) points: (3,0) ,(0,2), (2,2), (3,4)
how does (0,2) change? Answered by Penny Nom. 





A piecewise function 
20150425 

From uday:
f(x)={x^2+3x+2 / x+2, x(not equal to)=1
{4, x=1
how to find domain and how the graph looks like Answered by Penny Nom. 





Solve x=r(tsin(t)) for t 
20150228 

From David: I don't know how to write the function of t(x) by x=r(tsin(t)).
Can you teach me that? Answered by Harley Weston. 





A stone is dropped in a lake 
20150214 

From Wendy:
Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!
A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.
g(t) =
(b) Find a function f that models the area of the circle as a function of the radius r.
f(r) =
(c) Find f compose g.
f compose g = Answered by Penny Nom. 





Continuity on a closed interval 
20140921 

From Pragya: The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval,
but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's
limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help... Answered by Penny Nom. 





What is this function? 
20140417 

From Keta: What is this function?
12=2
6=1
6=1
0=0 Answered by Penny Nom. 





The locus of a point 
20140404 

From srishti: A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c . what is the locus of the point? Answered by Penny Nom. 





Graphing piecewise functions 
20140329 

From Rayven: Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to
graph piecewise functions. I know that you have already answered a question similar to this
(I did my research first) but it didn't completely help me on my homework. I have to graph
piecewise functions for the specified domains, and create a table for the absolute values.
I know that two bars around a number means absolute value (two bars around 2 makes it +2)
, but how do I graph and chart the absolute value for the following:
f(x)= x+3  for 5≤x≤3
And then graph and chart: (on a separate graph):
f(x)= {x if x≤0
{x+1 if x <0
thank you!
~Rayven Answered by Penny Nom. 





A limit with trig functions 
20140222 

From pearl: (what is the value of limit of x as it approaches 0 of sin8x divided by cos6x) Answered by Penny Nom. 





Water in a conical funnel 
20140211 

From Marcus: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Penny Nom. 





What does y= f(x) actually mean? 
20131231 

From John:
I don't understand how to pick coordinates for y=f(x).
I took a look at your answer to a previous question here:
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/monica2.html
What does y= f(x) actually mean? Answered by Penny Nom. 





Inverse trig functions 
20130519 

From ky: hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5.
And find the measure of all three angle using sin1, cos1, tan1.
I got really confuse, I'm taking the SAT pretty soon and it would be great
to get this... THANX Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





The continuity of f(x,y)=ln(x^2+y^2) 
20130217 

From anu: the question says we have to find the points in the plane where the function is continuous:
f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's
continuity.
what is to be done if we have to check continuity over the whole domain of the function?
please help . Answered by Harley Weston. 





What is the domain of f(x)=sin(ln(x))/ln(x)? 
20130206 

From Behrooz: Hi, the following problem may be interesting:
What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.
Best regards
Behrooz Answered by Penny Nom. 





An area bounded by lines 
20121216 

From sidra: find area bounded by functions:
y=x
y=2x
and y=5x Answered by Penny Nom. 





A function problem 
20121118 

From nahla: f: IN > IN
n > f(n)
for every n that belongs the IN : fof(x) = 4n  3
and for every n that belongs to IN f(2^n) = 2^(n+1) 1
Calculate f(993) Answered by Penny Nom. 





The derivative of y = sin (30º + x) 
20121107 

From Saskia: derivative of y = sin (30º + x) Answered by Harley Weston. 





Introductory algebra 
20121030 

From kevon: if x = 7 is used in the expression 2x + 5 what is the output Answered by Penny Nom. 





A function with 3 asymptotes 
20121019 

From rimoshika: find a function that have 3 Asymptotic : y=x/y=sinx/x=1 Answered by Penny Nom. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





The exponential function form f(x)=a^x 
20120813 

From Lucy: Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative? Answered by Penny Nom. 





The range of h(x) = 1/x 
20120811 

From Lucy: What is the range of the function: h(x)=1/x (and can you please explain why)? Answered by Penny Nom. 





A function from {a,b} to {p,q} 
20120810 

From Lucy: How can a function relate each element of a set with exactly one element of possibly the same set? Answered by Penny Nom. 





The inverse of y = x^2  2x 
20120420 

From Shona: How do I Find the inverse of the function y= x^2  2x ? Answered by Penny Nom. 





A uniform probability density function 
20120326 

From Noeline: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





The graph of a quadratic function 
20111227 

From Thomas: sketch a quadratic function with zeros at 3 and 1 Answered by Penny Nom. 





2 + f(x) and f(x) + 2 
20111121 

From Beth: Do you do y=2+f(x) the same way as if the 2 came after the equation such as y=f(x) +2 when graphing? Answered by Penny Nom. 





Composition of functions 
20110905 

From Jenna: Let f(x)=x^21 and g(x)=12x. Find the indicated values.
1. f(g(1)) and g(f(1))
Thanks,
Jenna Answered by Penny Nom. 





A step function 
20110822 

From Giovanna: An average school bus holds 45 people. Show a graph between the relationship of students who need bus transportation and number of buses required? Answered by Robert Dawson and Penny Nom. 





The domain of a function 
20110508 

From Minks: (x^2 + 1 / x^2 +2x  3 ) X ( x^2 9 / x^2  2x  3) Answered by Penny Nom. 





tanθ=1.192 
20110115 

From Adori: Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation.
a) tanθ=1.192
I do not understand how to find the second value of θ. Answered by Harley Weston. 





Can a function be both even and one to one? 
20101009 

From Tracy: Can a function be both even and one to one? Answered by Harley Weston. 





A pattern 
20100901 

From Hien: How to find the pattern in this function?
x=1, y=o
x=2, y=1
x=3, y=1
x=4, y=2
x=5, y=2
x=6, y=3
x=7, y=3 and so on... Answered by Tyler Wood. 





An inputoutput table 
20100607 

From Brian: Make an Input output table to represent the function. Use 0,1,2,3 as the Domain.
f(x)= 3+7x Answered by Harley Weston. 





graph y=(2x^23x)e^ax 
20100531 

From James: graph y=(2x^23x)e^ax Answered by Robert Dawson. 





f(x) = x + 3 
20100502 

From becca: Find the function value
F(1)if f(x)=x+3 Answered by Penny Nom. 





The intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





Write a function for the area in terms of x 
20100101 

From Almarie: Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet. Answered by Penny Nom. 





Maximizing the area of a rectangle 
20091217 

From rachel: A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area? Answered by Penny Nom. 





The inverse of f(x)=1/x^2 
20091022 

From Jasmine: how to solve f(x)=1/x^2 > find f1[x], than state if its a function Answered by Harley Weston. 





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





Graph 2x3y+15=0 
20090820 

From Diem: Graph 2x3y+15=0 Answered by Leeanne Boehm. 





An antiderivative problem 
20090813 

From Indrajit: ∫4e^x + 6e^x/(9e^x + 4e^x)dx = Ax + Bloge(9e2x  4) + C
then A=?......B=?.....C=?
plz solve it...."^" stands for "to the power of".... Answered by Harley Weston. 





Area under curve 
20090721 

From Morag: What is the area bounded by the curve y=X^2(2X) and the x axis between x=0 and x=2? Answered by Janice Cotcher. 





The integral of a to power x squared 
20090428 

From JIM: WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO
WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE
SOLVED : a to power x squared . is this still true ?
CURIOUS , JIM Answered by Robert Dawson. 





The integral of the square root of the sine function 
20090407 

From Indrajit: how to integrate this derivative???
∫√sinx Answered by Harley Weston. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





Trig functions without geometric data 
20090224 

From bob: I do not understand how it is possible to find the sine, cosine, or tangent of an angle if
there is no hypotenuse, opposite or adjacent side?! Answered by Robert Dawson. 





Intercepts in a Quadratic Function 
20090222 

From Barb: I have a question I need help with please. What are the number of x and y intercepts that quadratic function can have and why?
Thanks. Answered by Janice Cotcher. 





A piecewise function for monthly salary 
20090203 

From Josh: A sales rep for a drug company is paid on the following scale. His base salary is $1600 per month. He is also paid a commission of 2% of sales over $20,000. When his gross sales reach $30,000 he is then paid 4% on the amount above that until his sales reach $50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over $100,000 for the month. Set up a piecewise function for the information above. Answered by Harley Weston. 





The vertical line test 
20090126 

From bob: what is a Vertical line test Answered by Stephen La Rocque. 





What is f^1(3) when f(x)=2x1? 
20090103 

From Peter: how do you do functions like f^1(3) when f(x)=2x1? Answered by Penny Nom. 





A periodic function 
20081126 

From Ali: A periodic function f(x) has a period of 9, if(2)=3 and f(5)=13, determine the value of f(11)?
tks /rgrds
Ali Answered by Penny Nom. 





A conical funnel 
20081112 

From Rachael: Hello, I am a 10th grader in AP Calc, and can not figure out this question:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Harley Weston. 





Is it possible to a function to be both even and odd ? 
20080928 

From Mohammed: Is it possible to a function to be both ( Even and Odd ) Answered by Harley Weston. 





What is the derivative of (2^sinx)/(logbase4(2x+1))? 
20080916 

From Jesse: What is the derivative of (2^sinx)/(logbase4(2x+1)) Answered by Harley Weston. 





Limit as it Approaches a Constant 
20080916 

From Brooks: what is the limit as x approaches 10 for f(x) = sqrt(x1) = 3 pleeeeeaase help me out here Answered by Janice Cotcher. 





Function or Not? 
20080822 

From Katie: Determine whether y is a function of x:
[(x^2)y](x^2)+(4y)=0
....thx Answered by Janice Cotcher. 





Graphing a piecewise function 
20080812 

From Shanti: how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to 2 and less than 1
2 u if u is greater than or equal to 1 and less than 4 Answered by Penny Nom. 





A linear function 
20080807 

From Warren: What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function?
How will you transform y=square root of 3 x + 1 in standard form Ax+By=C? Answered by Penny Nom. 





The product of the digits of a four digit number 
20080726 

From Pete: I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property? Answered by Stephen La Rocque. 





Express as a function of x 
20080714 

From Rita: Express the area A of an isosceles right triangle as a function of x of one of the two equal sides.
NOTE: I always see the phrase "Express as a function of x" in math textbooks.
What exactly does that phrase mean?
I also have seen it written as "Express in terms of x." Answered by Penny Nom. 





Composition of two functions 
20080704 

From Kristian: f(x)= the square of x add to 1 and g(x)=1/x
find: (f o g)x Answered by Penny Nom. 





g(m1,2n)+n 
20080607 

From Florence: What does g(m1,2n)+n for m>0, n>=0 mean. Answered by Penny Nom. 





The number of hours of daylight 
20080603 

From Marilyn: Hi, could you please help me with this question?
In a city (in the Northern Hemisphere) the minimum
number of hours of daylight is 9.6 and the maximum
number is 14.4. If the 80th day of the year (March
21) has 12 hours of daylight, determine a sine
function which gives the number of hours of
daylight for any given day of the year. (Jan 1 = 1,
Jan 2 = 2, etc).
Thank you! Answered by Harley Weston. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





Adding rational functions 
20080429 

From Jonathon: 1/(x+3) + 1/(x^2+5x+6) = Answered by Penny Nom. 





Two function problems 
20080410 

From keith: find the domain: F(x)= 1/ {ln (x+5)  ln (7x)}
find the inverse: g(t)= sqrt {23 ln (1t)} Answered by Penny Nom. 





cosec [arccos (1/y)] 
20080409 

From Tom: I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is? Answered by Penny Nom. 





The average rate of change 
20080329 

From Tom: For the function x/3x1 find the average rate of change between the interval x=1 and x=5? Answered by Harley Weston. 





A function satisfying f(x) + 2f(1/x) = x 
20080325 

From Joan: Let f be a function satisfying f(x) + 2f(1/x) =x for all real numbers (x does not equal 0)
a) Find f(1) justify your answer
b) Find f(2) justify your answer Answered by Penny Nom. 





Inverses of functions 
20080313 

From jess: if g(x)=2x+3 find g^1(g(4))
how do I sovle I cant's figure out what to do with the 4 Answered by Stephen La Rocque. 





Saving to buy a coat 
20080309 

From alayna: Jackie is saving her money to buy a coat that costs $121. If she already has $61 and saves
$15 each week, in how many weeks can she buy the coat ? Make a function table to answer the
question. Answered by Penny Nom. 





Composition of functions 
20080307 

From sharon: Find FoG(x)
F(x)= the square root of x9
G(x)= x^2
and also find GoF and their domains Answered by Penny Nom. 





F( x  2) = (x + 3)/ (x  4) 
20071220 

From Sean: If F( x  2) = (x + 3)/ (x  4) , then F(5) = 10/3
How do you solve this problem and what section of calculus can I learn the technique to solve this type of problem? Answered by Stephen La Rocque. 





Transformations and compositions 
20071129 

From mary: Is there any possible relationship between composite functions and the concept of function transformations? Answered by Harley Weston. 





Maximize his profit 
20071112 

From apoorva: During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day.
a. Find the demand function, assuming it is linear.
b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Answered by Penny Nom. 





Family of functions 
20071112 

From Russell: Consider the family of functions
f(t)= Asin3t + Acos3t +Bsin8t + Bcos8t
find exact values of parameters A and B so that f(0) = 2 and f ' (0) = 1 Answered by Stephen La Rocque. 





Domain and range 
20071012 

From Dawn: Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help. Answered by Penny Nom. 





Inverses of Quadratic Functions 
20071011 

From Elliot: I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated. Answered by Steve La Rocque and Harley Weston. 





The average rate of change of a function 
20071011 

From vern: Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]? Answered by Harley Weston. 





Maximizing profits II 
20071005 

From a student: Suppose there are three firms with the same demand function. The function is Q=100040P. Each firm also a a cost function.
Firm 1: 4000+5Q,
Firm 2: 3000+5Q,
Firm 3: 3000+7Q.
What price should each firm charge if it wants to maximize profits. Answered by Harley Weston. 





Irrational functions 
20071001 

From alicia: i have a question about irrationals functions.
i have been using them quite some time now, but i wonder where they can be found in daily life?
i hope you can help me, Answered by Harley Weston. 





Is x/y + y/x = 2 a function? 
20070906 

From Farzan: Is x/y + y/x = 2 a function or not. Answered by Penny Nom and Stephen La Rocque. 





Relations and functions 
20070816 

From virginia: determine whether each relation is a function provide reasons for identifying relation
(3, 4) (5, 9) (9, 9) (2, 3)
(0, 0) (0, 1) (1, 4) (2, 4)
(2, 1) (4, 5) (8, 4) (1, 0)
(8, 3) (8, 0) (7, 7) (4, 7) Answered by Steve La Rocque. 





The domain and range of a quadratic function 
20070717 

From Linda: I have been trying to solve this problem but I'm unable to figure it out. How do I find the domain and range of
y=(x+1)^23? Please explain...thanks! Answered by Stephen La Rocque and Penny Nom. 





Trig functions for angles not between 0 and 90 degrees 
20070716 

From Tim: My question: Why is the value of a trigonometric function, the same, for an angle over 90 degrees and its reference angle?
How are the angle and its reference related? Do they both form a triangle that has equal sides? Answered by Penny Nom. 





Derivative of a Function 
20070709 

From Bob: What is the derivative of the function a sub n = [n/(n+1)]^n ? Answered by Stephen La Rocque. 





Period of a sum of trig functions 
20070617 

From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque. 





Express a certain variable as a function of another variable 
20070612 

From Gilligan: The volume V of a right circular cone is V = (1/3)pi(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.
I see the phrase "express a certain variable as a function of another variable" a lot in math books.
What exactly does that mean?
Is there another way to say the same thing? Answered by Stephen La Rocque. 





Composition functions 
20070612 

From Gilligan: Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start. Answered by Stephen La Rocque. 





The limit of a rational function 
20070528 

From Imad: 3 _______ 3 _______
lim \/ 1 + x  \/ 1  x
x>0  
x Answered by Penny Nom. 





What does inverse graph represent? 
20070330 

From san: what does inverse graph represent? Answered by Penny Nom. 





Is the inverse of a function always a function? 
20070329 

From San: Is the inverse of a function always a function? Please justify. Thank You! Answered by Penny Nom. 





What makes a relation a function? 
20070321 

From san: What makes a relation a function? Answered by Haley Ess. 





An even function 
20070307 

From Dana: Find a function t(x) such that t(x)/x+3 = y is an even function Answered by Haley Ess. 





An odd function 
20070306 

From Dana: If g(x) has a domain of all real numbers, name one point on a graph and explain why it must be there. g(x) is an odd function. Answered by Penny Nom. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





y = f(x) and y = 2f(x6) 
20070302 

From carl: if P(4,5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x6). Answered by Penny Nom. 





Inputoutput table 
20070110 

From Richard: Question is make an input  output table for the function using the domain 0,1,2,3,4, Then state the range of the function.
y =x + 8 ?
y =0.4x +3 ? Answered by Penny Nom. 





y = 5 x  3 
20070110 

From Richard: Question is the function y = 5 x  3 for the given value of x 7 , 1 or 4 Answered by Stephen La Rocque and Penny Nom. 





Composition of functions 
20061119 

From RJ: Let f0(x) = 2/2x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque. 





Composition of functions 
20061118 

From Oryan: Given f(x)=2x^3 and g(x)4x5, find g(f(1)) Answered by Stephen La Rocque. 





Piecewise functions 
20061108 

From Kait: We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says: f(x){2x+1, if x <1 f(x){x+4, if x is greater than or equal to 1. Answered by Penny Nom. 





Piecewise functions 
20060924 

From Claudia: hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it.
my problem is
g(x){x+2 if x <2}
g(x){2x  1 if x> or = 2} Answered by Penny Nom. 





The zeros of a function 
20060612 

From Sky: find all the real zeros of the function:
f(x)=2x^{3} + 4x^{2 } 2x  4 Answered by Stephen La Rocque. 





Geometric sequence and basic functions (graphs) 
20060420 

From Marlene: Which of the basic functions is related to the geometric sequence:
Linear, Quadratic, Rational, or Exponential?
Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque. 





Finding the inverse of a function 
20060412 

From Sam: If g(x) = 2x+3/5 then how do I find the inverse? Answered by Walter Whiteley. 





An exponential function 
20060403 

From Meadow: The graph of an exponential function passes through the points (0,1) and (4,10) find the constant of growth or decay. State the function. Answered by Stephen La Rocque. 





Piecewise functions 
20060321 

From Kris: First Problem:
Southeast Electric charges .09 cents per kilowatthour for the first 200 kWh.The company charges .11 cents per kilowatthour for all electrical usage in excess of 200 kWh. How many kilowatthours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?
Second Problem:
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs overtime worked. Again I don't know how to set up the equation to come up with the answer.
I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful. Answered by Penny Nom. 





sinh(i/2) 
20060209 

From Louis: How can you set up an equation to find sinh(i/2) Answered by Penny Nom. 





fog 
20051112 

From Janice: I am having problem with the (fog) function
(fog) (x). Given f(x)= 2x^{2} ; g(x)= 34x Answered by Penny Nom. 





Painter's caps 
20051019 

From Duk: The equation C=10 +2n represents the cost in dollars, C, for n painter's caps advertising the walkathon. Which pair of values could represent a number of caps and the cost for that number of caps, (n, C)?
(0, 10) (7, 24) (15, 30) Answered by Penny Nom. 





A piecewise function 
20050915 

From Duncan: A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Answered by Penny Nom. 





y = log(x) + x. Solve for x. 
20050826 

From Alain:
I have the following equation:
y = ln(x) + x
How do I solve for x?
Answered by Penny Nom. 





Labour efficiency 
20050823 

From Rob:
The problem, on the surface, seems very simple and yet has created some controversy among a group of accountants. The problem itself has to do with labour efficiency rates and only involves two variables; standard working hours, and actual working hours. The difficulty lies in deriving an efficiency % from these two numbers.
Standard working hours or the targeted number of labour hours required to produce one widget, which I will represent as "s". Actual working hour or the actual number of labour hours require to produce one widget, which I will represent as "a". Labour efficiency I will represent with "E". The prevailing calculation with which I have a problem with is this:
s/a=E or if s=3000, and a=4000 then 3000/4000=75%
What bothers me about the calculation is that the standard hours get represented as a percentage of the actual hours and in my opinion changes the focus of the calculation from standard or target, where it should be, to the actual hours. I cannot define why, but this just seems inherently wrong to me.
The calculation that I use:
(1+((sa)/s))=E or if s=3000, and a=4000 then (1+((30004000)/3000))=66.67%
My calculation is like a %change from standard calculation. However, there is something that also concerns me about my calculation.
If you substitute 100 for a and 50 for s, then you come to a quandary, because if you plug those numbers into the second equation the result is of course zero % efficient which doesn't sit right with me either. If you plug them into the first calculation you get 50% efficiency which doesn't really seem to work either, because you require 100% more hours to do the same work in this case. ???
Is the first calculation correct? Am I missing something altogether? Are both calculations off base? Answered by Harley Weston. 





The range of a function 
20050821 

From Kelsey: What is the range of the function f(x) = 4x  6 when the domain is {3,1,1,3,5}? Answered by Penny Nom. 





Rational functions 
20050405 

From Nicole: My name is Nicole and I am a teacher at Weyburn Comprehensive School. I am currently teaching both Math B30 and Calculus 30 at the school and I have a question about rational functions. I know that if a rational function (by definition) has common factors in the numerator and the denominator then it is not a rational function (math b30) however in calculus this common factor creates a hole in our graph. Can you explain to me why a common factor or constant does not give us a rational function? Answered by Penny Nom and Leeanne Boehm. 





Profit 
20050110 

From Abraham: The profit a coat manufacturer makes each day is modeled by the equation P(x)=x2+120x2000, where P is the profit and x is the price for each coat sold.For what values of x does the company make a profit?
I don 't understand this problem(how to do it) and hope you can help me. Answered by Penny Nom. 





The points of intersection of two graphs 
20041105 

From Benjamin: How do I find the points of intersection of the two functions:
1) y = 2  ex
2) y = 1 + x2 Answered by Harley Weston. 





f(x) = x4 if x<2 
20040921 

From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Answered by Penny Nom. 





An inverse 
20040909 

From Hillary: I cannot figure out the inverse of this function.
f(x)= 1/2x 1 Answered by Penny Nom. 





Limits and composite functions 
20040807 

From Sue: I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x>0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
Sue Answered by Penny Nom. 





The intersection of two graphs 
20040728 

From JJ: Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Answered by Penny Nom. 





The inverse of a quintic function 
20040722 

From A student: I'm really having trouble finding out the inverse of this quintic equation. F(X)= X^{5}+3X^{3}+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out. Answered by Penny Nom. 





A probability density function 
20040414 

From A student: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 <= x <= 12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





Polynomials 
20040125 

From Bruce:
A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = a_{n}x^{n} + a_{n1}x^{n1} + ... + a_{1}x + a_{0}
The value of n must be an nonnegative integer. That is, it must be
whole number; it is equal to zero or a positive integer.
The coefficients, as they are called, are a_{n}, a_{n1},
..., a_{1}, a_{0}. These
are real numbers.
Questions:
 why must n be positive?
 what are some historical facts
about the evolution of the definition?
Answered by Harley Weston. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





A parabola 
20031024 

From Delores: Given the vertex (4, 2) y intercept = 6 find if/where the parabola crosses the x axis? Answered by Penny Nom. 





Domain of a function 
20031014 

From Karim: Find the Domain of the Function H(x) = Log3 (4x + 7)10 H(x) = log base 3 times 4X plus 7 minus 10 i am having problem solving these kinds of problems. Answered by Penny Nom. 





Graphing a piecewise function 
20030824 

From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom. 





A rule with a variable 
20030824 

From Crystal: what is a rule with a variable Answered by Penny Nom. 





Two precalculus problems 
20030804 

From Kate:
Please help me verify the identity: cos2x(sec2x1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3x Answered by Penny Nom. 





The domain of 1/g(x)  5 
20030703 

From Barbara: If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x)  5? Answered by Penny Nom. 





y = 1  sin(x + 60) 
20021210 

From Eman: Sketch the graph of y = 1  sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis. Answered by Penny Nom. 





A function that is onto but not onetoone where f:N>N 
20021206 

From Lisa: A function that is onto but not onetoone where f:N>N Answered by Penny Nom. 





Performance reviews 
20021121 

From Lara: Perhaps you can help. He's doing performance reviews at work. The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year. The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year. How do I solve for the other performance review numbers. Answered by Penny Nom. 





Differentiating inverses 
20021120 

From Amy: f(x)= x^{3}+x+1, a=1 find g'(a) (g = f^{ 1}). I am having trouble finding g(a). Answered by Penny Nom. 





A functional equation 
20021014 

From Rob: Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n)
b) f(f(n))=3(n) Answered by Claude Tardif. 





A linear function 
20020909 

From Chad: If y = 9x  13 does it represent a linear function? And if it does what is its slope and is it a direct variation? Answered by Peny Nom. 





Domain of a function 
20020720 

From Andy: I'm having difficulty in finding the domain of 1/(x^{2} 2x + 4) one over x squared minus 2 x plus 4. Answered by Penny Nom. 





Functions and relations 
20020425 

From Erin: Here's a few math problems that might drive a person insane ;)  If 2f(x)  3f(1/x) = x^2 what is f(2)?
 What are the domain and range of the following relations?
 x^2  4y^2 = 25
 4x^2 + 9y^2 = 36
 The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?
 Prove the identity. 1+sinx + cosx/ 1sinx + cosx = 1+sinx / cosx
Answered by Penny Nom. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 





Zeta[2]=(Pi^{2})/6 
20020202 

From alex: Can you please tell me a proof that Zeta[2]=(Pi^{2})/6 Answered by Chris Fisher. 





Catenary 
20020102 

From Jason: I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary. The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the yaxis. Any help you can provide would be greatly appreciated. Answered by Harley Weston. 





Composition of functions 
20011216 

From Paula:
 if f(x)= 3x1 and g(x)= 1/2x + 3 find fog(2)
 find the values of x for which tanx=0
Answered by Penny Nom. 





Dual spaces 
20011126 

From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. Answered by Doug Farenick. 





Some functions without numbers 
20011116 

From A student: I have a worksheet that is about functions. It doesn't only use numbers. I need help to figure out the function and the solution to how the answer is solved. Answered by Claude Tardif. 





Symmetry of f(x) = ax^n 
20011018 

From Mohammed: a function of the form f(x)=ax^{n}, where a doesn't equal 0 and n is a positive integer is called a power function . how is the exponent in the equation of a power function related to the symmetry of its graph? Answered by Penny Nom. 





A function or not a function? 
20011018 

From Christian: Which are the following are not functions?  y = x^{2}
 y = x^{3}
 x = y^{2}
 y = 3
Answered by Leeanne Boehm. 





Inverting a function 
20010930 

From Brandie: Could you please tell me what is the basic guideline for inverting a function Example: S(R)=2PiRal V(R)=PiR(squared)bl R(V)=? Answered by Claude Tardif. 





A quadratic function 
20010510 

From A parent: A quadratic function is given by f:xax^{2}+b
If the two points A(2, 2) and B (0, 8) are on the graph of the function, then find a and b. Answered by Penny Nom. 





National consumption function 
20010509 

From Brian: If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Answered by Harley Weston. 





The average value of a continuous function 
20010508 

From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston. 





A sequence defined recursively 
20010501 

From A student: A sequence s is defined recursively as follows: s_{0}=1 s_{1}=2 s_{k}=2s_{k2} for all integers  Compute s2,s3,s4... to guess an explicit formula for the sequence sk. Answered by Penny Nom. 





Choosing a car 
20010428 

From Ashley: THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? Answered by Penny Nom and Andrei Volodin. 





The domain of a function 
20010408 

From Mina: Let f(x) = (2x^{2}+3x17)/(x+5) What is the domain of f? What are the values of x for which f'(x) does not = 0? Answered by Harley Weston. 





f(x), f(x) + 2, f(x +2) 
20010404 

From Monica: Could you explain to me how one should go about graphing functions such as f(x), f(x+2), and so on. Also, how should you explain things such as constants and relationships among functions? Answered by Penny Nom. 





Domain and Range and Zeros 
20010227 

From Beth: 1. f(x)=152xx^{2} 2. g(t)=square root of 4t^{2} 3. y=t3/t^{2}t6 Answered by Penny Nom. 





Adding functions 
20010219 

From Jackie: f(x) = x^{2} + 1; g(x) = x^{2}  1 find a) ((f+g) of h)) (x) b) ((fg) of h)) (x) c) ((f of h)  (g of h)) (x) Answered by Penny Nom. 





Range of a function 
20001121 

From David Bell: Given a rational function such as f(x) = (8x3)/(4x1). How can the range be found. Answered by Penny Nom. 





Domain of a function 
20001115 

From Mickey: state any restrictions on the domain of the function. y = 5x  12 over 27x + 6 x does not equal what________? Answered by Penny Nom. 





Graphing F(x) = 3^{x} 
20001106 

From Jose: graph the exponential problem F(x)=3^{x} Answered by Harley Weston. 





An equation involving x to the x 
20000722 

From Joy Peter: I am joy, a teacher teaching Maths at the secondary level and while solving a sum came to this stage when i got x^{x} (1 + log x) = 0, by which we can conclude that x^{x} = 0 or 1 + log x = 0. If x^{x} = 0, than what should be the value of x? I feel that the value of x should then be 0 (zero) but then how do I explain this to the students as we also know that anything to the power of 0 is 1 but here 0 raised to 0 is 1. If this is not defined then how do I explain this? Answered by Penny Nom. 





Calculus Research Questions 
20000522 

From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston. 





Graphing a linear function 
20000517 

From Chelsea: I need help with grahing linear functions.If you could email me back the basics and how tos I would be much appriciative. Answered by Penny Nom. 





sin(7pi/12) 
20000504 

From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts. 





Graphing cube roots 
20000427 

From Heather Jones: What do the graphs of cube roots look like? Answered by Walter Whiteley. 





Functions that satisfy f' = f 
20000316 

From Kevin Palmer: Recently my calculus teacher asked his students to try and find any functions whose derivatives where the exact same as the original function. The only function then I have determined that statement to be accurate in is all the natural exponential functions. Ex. f(x) = e^{x}, f'(x) = e^{x} If possible could you please email me all the functions that you can find in which the original function and its derivative is identical. Answered by Claude Tardif. 





Irrational algebraic functions 
20000221 

From Bucky Cadena: Here is the multipart problem: Given f(x) = x3* squareroot of x + 4 What does the f(x) intercept equal Find the two values for which f(x) = 5 Find the one value for which f(x) = 3 Answered by Harley Weston. 





Functions 
20000123 

From Tara: Hi my name is Tara, I have two math problems that I need help with in my calculus math class.  If f(x)= x  2 show that (x+3)f(x)(x+2)f(x+1)+4=0
 Graph this function and use the graph to determine the range y=2x^{2}  8x  3
Answered by Harley Weston. 





The limit of f(x)/x 
20000122 

From Laurent Jullien: I would appreciate help to prove that a twice continuously differentiable convex function from R+ to R has the property that f(x)/x has a limit when x tends to infinity. Answered by Claude Tardif. 





Domain of a function 
20000119 

From Stacey Hutchison:
What is the domain of: f(x) = 1/(x + 4) Answered by Patrick Maidorn. 





Functions 
20000106 

From Tori Morris: Consider the function f(x)=x^{2}3. Which of the following are true?  f(1)>f(0)
 f(2)>f(3)
 f(2)=f(2)
 f(1)=f(3).
More than one answer can be true. Answered by Penny Nom. 





Period 
19991228 

From Mahdawi: I have attached a diagram of the graph, and I need to find out its period. I really don't understand how to do so, please help! Answered by Harley Weston. 





Three algebra problems 
19991228 

From Stephanie Branton:
 If P represents the product of all prime numbers less than 1000, what is the value of the unit's digit of P?
 Do any real numbers a and b exist such that: ln(a+b)=ln a + ln b? if so, what are they?
 Define a function by: f(x)=1/1x where x is not equal to 0,1. what is f(f(f(a)))?
Answered by Harley Weston. 





Graph of a sine function 
19991223 

From Pierre: Given; amplitute:1 period: 540 Phase shift: 60 degree,right I am ask to right the equation: sin 2/3 (value 60degree) When I am asked to graph the equation, the period is mixing me up. Answered by Harley Weston. 





polynomial functions 
19991119 

From Quinn:
 Without fully factoring the following show that they all have the same zeros:
I: x^{4}x^{2}+2x+6 II: x^{4}+x^{2}2x6 III: 4x^{4}+4x^{2}8x24 IV: 10x^{4}10x^{2}+20x+60  When P(x)=x^{3}3x^{2}+5x+1 and G(x)=x^{3}2x^{2}x+10 are each divided by(xa) the remainders are equal. At what coordinate point does the graph of P(x) intersect G(x)?
Answered by Walter Whiteley. 





Domain and Range of a Function 
19991114 

From Michelle Mellott: How do you find the range of the following function: 2y^{2}/(y^{2}+5y+6)?? I know the domain is x not equalled to 2, 3. How can one easily find the range? Answered by Harley Weston. 





Inverses of functions 
19991101 

From Leanne Hickey: Let f(x) = 2x^{2} 3x + 2. Find f^{1}(4) given the fact that f(2) = 4. So the question is finding the inverse of 4, he said it's easier than it looks. Answered by Penny Nom. 





Piecewise functions. 
19991020 

From Jenny: How do you figure out a piecewise function by hand? e.x. ( 2x (if x is not equal to 0) f(x)=< ( 0 (if x is not equal to 0) Answered by Harley Weston. 





Even and Odd Function 
19990617 

From Kent: There is one function with the domain of all real numbers that is both even and odd. Please give me the answer to this question before I go insane. Answered by Penny Nom. 





Points on a Graph 
19981003 

From Nouver Cheung: If the point P(3,2) is on the graph of y=f(2x1), what point must be on y=f(x)3? Answered by Harley Weston. 





Polynomials 
19980113 

From Sarah Storkey: Hi, My name is Sarah, My question is at the junior level. My question is, what is a polynomial? Answered by Harley Weston. 





The Range of a Function. 
19970912 

From Karel Marek: Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..The question is: Indicate the domain and range for this: y = sqr(x9) (Square root of) The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject.. But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject.. Can you explain this... ?? Answered by Chris Fisher. 





Square Roots and Functions. 
19970423 

From Ed: 1. In most texts the solution to a question such as square root x = 6 is x is undefined. Yet when teaching to solve xsquared = 36 x = +6 or 6 There appears to be a contradiction here. My question is when, where and why do we use the principle square root, not both + and ? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots. 2. Are there any simple rules for determining whether equations are functions without graphing them and doing a vertical line test? Answered by Harley Weston. 





A Functional Equation. 
19970226 

From Ronald Lui: Find all functions f:S > S statisfying the two conditions: 1)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S 2)f(x)/x is strictly increasing on each of the interval 1 Answered by Saroop Kaul and Chris Fisher. 





Grade nine problem solving 
19960311 

From Azmat Hussain: Can math problems be actually fun and engaging? Answered by Diane Hanson. 





Application surjective 
19990930 

From Charass: je suis étudiant en premiere année de deug et je cherche apres une definition si vous pouviez m'aider, ça serait sympa. qu'est ce qu une application subjective? Answered by Claude Tardif. 

