Topic: functions list of topics
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	2 + f(x) and f(x) + 2		2011-11-21
		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		2011-09-05
		From Jenna: Let f(x)=x^2-1 and g(x)=1-2x. Find the indicated values. 1. f(g(1)) and g(f(1)) Thanks, Jenna Answered by Penny Nom.
	tanθ=1.192		2011-01-15
		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.
	f(x) = x + 3		2010-05-02
		From becca: Find the function value F(1)if f(x)=x+3 Answered by Penny Nom.
	Maximizing the area of a rectangle		2009-12-17
		From rachel: A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area? Answered by Penny Nom.
	y=2x+1 and y=2x-1		2009-08-28
		From MARICELA: Need help of how to work this problems y=2x+1 and y=2x-1 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.
	The integral of a to power x squared		2009-04-28
		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		2009-04-07
		From Indrajit: how to integrate this derivative??? ∫√sinx Answered by Harley Weston.
	Trig functions without geometric data		2009-02-24
		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.
	The vertical line test		2009-01-26
		From bob: what is a Vertical line test Answered by Stephen La Rocque.
	What is f^-1(3) when f(x)=2x-1?		2009-01-03
		From Peter: how do you do functions like f^-1(3) when f(x)=2x-1? Answered by Penny Nom.
	What is the derivative of (2^sinx)/(logbase4(2x+1))?		2008-09-16
		From Jesse: What is the derivative of (2^sinx)/(logbase4(2x+1)) Answered by Harley Weston.
	Composition of two functions		2008-07-04
		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.
	The number of hours of daylight		2008-06-03
		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		2008-05-03
		From keith: please help me find the inverse of this function: h(t) = 2 + 4 ln(1-5t) Answered by Stephen La Rocque.
	Adding rational functions		2008-04-29
		From Jonathon: 1/(x+3) + 1/(x^2+5x+6) = Answered by Penny Nom.
	Two function problems		2008-04-10
		From keith: find the domain: F(x)= 1/ {ln (x+5) - ln (7-x)} find the inverse: g(t)= sqrt {2-3 ln (1-t)} Answered by Penny Nom.
	A function satisfying f(x) + 2f(1/x) = x		2008-03-25
		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.
	Composition of functions		2008-03-07
		From sharon: Find FoG(x) F(x)= the square root of x-9 G(x)= x^2 and also find GoF and their domains Answered by Penny Nom.
	F( x - 2) = (x + 3)/ (x - 4)		2007-12-20
		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		2007-11-29
		From mary: Is there any possible relationship between composite functions and the concept of function transformations? Answered by Harley Weston.
	Family of functions		2007-11-12
		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.
	Irrational functions		2007-10-01
		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.
	Relations and functions		2007-08-16
		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.
	Trig functions for angles not between 0 and 90 degrees		2007-07-16
		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		2007-07-09
		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		2007-06-17
		From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque.
	Composition functions		2007-06-12
		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.
	Is the inverse of a function always a function?		2007-03-29
		From San: Is the inverse of a function always a function? Please justify. Thank You! Answered by Penny Nom.
	y = f(x) and y = 2f(x-6)		2007-03-02
		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(x-6). Answered by Penny Nom.
	Composition of functions		2006-11-19
		From RJ: Let f0(x) = 2/2-x 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		2006-11-18
		From Oryan: Given f(x)=-2x^3 and g(x)-4x-5, find g(f(-1)) Answered by Stephen La Rocque.
	Piecewise functions		2006-11-08
		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		2006-09-24
		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		2006-06-12
		From Sky: find all the real zeros of the function: f(x)=2x3 + 4x2 - 2x - 4 Answered by Stephen La Rocque.
	Piecewise functions		2006-03-21
		From Kris: First Problem: Southeast Electric charges .09 cents per kilowatt-hour for the first 200 kWh.The company charges .11 cents per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours 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 over-time 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)		2006-02-09
		From Louis: How can you set up an equation to find sinh(i/2) Answered by Penny Nom.
	fog		2005-11-12
		From Janice: I am having problem with the (fog) function (fog) (x). Given f(x)= 2x2 ; g(x)= 3-4x Answered by Penny Nom.
	y = log(x) + x. Solve for x.		2005-08-26
		From Alain: I have the following equation: y = ln(x) + x How do I solve for x? Answered by Penny Nom.
	Labour efficiency		2005-08-23
		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+((s-a)/s))=E or if s=3000, and a=4000 then (1+((3000-4000)/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		2005-08-21
		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		2005-04-05
		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		2005-01-10
		From Abraham: The profit a coat manufacturer makes each day is modeled by the equation P(x)=-x2+120x-2000, 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		2004-11-05
		From Benjamin: How do I find the points of intersection of the two functions: 1) y = 2 - e-x 2) y = 1 + x2 Answered by Harley Weston.
	Limits and composite functions		2004-08-07
		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		2004-07-28
		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.
	Polynomials		2004-01-25
		From Bruce: A polynomial is defined as Polynomial functions are functions that have this form: f(x) = anxn + an-1xn-1 + ... + a1x + a0 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 an, an-1, ..., a1, a0. 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		2003-12-02
		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.
	Graphing a piecewise function		2003-08-24
		From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom.
	Two precalculus problems		2003-08-04
		From Kate: Please help me verify the identity: cos2x(sec2x-1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3-x Answered by Penny Nom.
	The domain of 1/g(x) - 5		2003-07-03
		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)		2002-12-10
		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.
	Differentiating inverses		2002-11-20
		From Amy: f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a). Answered by Penny Nom.
	Functions and relations		2002-04-25
		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/ 1-sinx + cosx = 1+sinx / cosx Answered by Penny Nom.
	Composition of functions		2002-04-06
		From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 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(-x2 - 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.
	Composition of functions		2001-12-16
		From Paula: if f(x)= 3x-1 and g(x)= 1/2x + 3 find fog(2) find the values of x for which tanx=0 Answered by Penny Nom.
	Some functions without numbers		2001-11-16
		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		2001-10-18
		From Mohammed: a function of the form f(x)=axn, 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.
	Inverting a function		2001-09-30
		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.
	f(x), f(x) + 2, f(x +2)		2001-04-04
		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		2001-02-27
		From Beth: 1. f(x)=15-2x-x2 2. g(t)=square root of 4-t2 3. y=t-3/t2-t-6 Answered by Penny Nom.
	Adding functions		2001-02-19
		From Jackie: f(x) = x2 + 1; g(x) = x2 - 1 find a) ((f+g) of h)) (x) b) ((f-g) of h)) (x) c) ((f of h) - (g of h)) (x) Answered by Penny Nom.
	Range of a function		2000-11-21
		From David Bell: Given a rational function such as f(x) = (8x-3)/(4x-1). How can the range be found. Answered by Penny Nom.
	Graphing F(x) = 3x		2000-11-06
		From Jose: graph the exponential problem F(x)=3x Answered by Harley Weston.
	Graphing a linear function		2000-05-17
		From Chelsea: I need help with grahing linear functions.If you could e-mail me back the basics and how tos I would be much appriciative. Answered by Penny Nom.
	sin(7pi/12)		2000-05-04
		From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts.
	Functions that satisfy f' = f		2000-03-16
		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) = ex, f'(x) = ex 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		2000-02-21
		From Bucky Cadena: Here is the multipart problem: Given f(x) = x-3* 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		2000-01-23
		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=2x2 - 8x - 3 Answered by Harley Weston.
	The limit of f(x)/x		2000-01-22
		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.
	Functions		2000-01-06
		From Tori Morris: Consider the function f(x)=x2-3. 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.
	Three algebra problems		1999-12-28
		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)=1/1-x where x is not equal to 0,1. what is f(f(f(a)))? Answered by Harley Weston.
	polynomial functions		1999-11-19
		From Quinn: Without fully factoring the following show that they all have the same zeros: I: x4-x2+2x+6 II: -x4+x2-2x-6 III: -4x4+4x2-8x-24 IV: 10x4-10x2+20x+60 When P(x)=x3-3x2+5x+1 and G(x)=x3-2x2-x+10 are each divided by(x-a) the remainders are equal. At what coordinate point does the graph of P(x) intersect G(x)? Answered by Walter Whiteley.
	Inverses of functions		1999-11-01
		From Leanne Hickey: Let f(x) = 2x2 -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.		1999-10-20
		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		1999-06-17
		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		1998-10-03
		From Nouver Cheung: If the point P(-3,2) is on the graph of y=f(2x-1), what point must be on y=f(x)-3? Answered by Harley Weston.
	Polynomials		1998-01-13
		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.
	Square Roots and Functions.		1997-04-23
		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.

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