







A straight line graph 
20200226 

From Penehafo: I have a problem of drawing a straight line graph by the equation y=2x1 Answered by Penny Nom. 





A system of inequalities 
20200201 

From Isaac: Austin has x nickels and y dimes, having a maximum of 15 coins worth a minimum of $1 combined. No more than 4 of the coins are nickels and no less than 11 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution. Answered by Penny Nom. 





Investigating y = (2)^x 
20200113 

From Gonzalo: This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph $y=(2)^x.$
The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday. Answered by Harley Weston. 





y = x  1 
20181130 

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





Graphing y = 2x  1 
20180312 

From Himanshu: Hi I Himanshu I having 1 doubt on 1 question this question of graph how to draw y=2x1 Answered by Penny Nom. 





The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





The distance between the origin and a moving point on a graph 
20171016 

From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom. 





A pie chart 
20161205 

From vickie: Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant 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. 





A circle graph 
20150406 

From Davis: i don't know how to answer this question. please help!
a survey about student government shows the following results
110 like the program
120 think the program is unnecessary
210 plan on running for student government next year
if this information is put in a circle graph,what is the central angle for the students who like the program? Answered by Penny Nom. 





A piecewise graph 
20140510 

From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0500 units cost 17 cents per unit
5001500 units cost $85 plus 10 cents for each unit in the excess of 500
1500 or more units cost $185 plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units 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 circle graph 
20140306 

From Caitlyn: I need to find the measure of the central angle that represents the amount of time spent on each activity.
My question includes a circle graph with the following: Sleep 31%, Other 15%, Entertainment 18%, Errands 7%,
Work 20%, and Food 9%. Answered by Penny Nom. 





The graph of y=2x+4 
20140218 

From tyler: y=2x+4 graph Answered by Penny Nom. 





The graph of f(x)=x^24 
20140207 

From Allison: Graph f(x)=x^24 and give the five point of the x/y intercepts. 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. 





How do I graph y=2x1? 
20131207 

From cindy: How do I graph y=2x1? Answered by Penny Nom. 





How can we draw the equation "x+y=1" in 3d? 
20130503 

From shimaa: how can we draw the equation "x+y=1" in 3d Answered by Robert Dawson. 





Solve sin 3x = 0.1254 with x between o and 360 degrees 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Solve sin 3x = 0.1254 with 0 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Plotting y=f(x)+2 
20130121 

From Gavin: how would you plot y=f(x)+2 Answered by Penny Nom. 





A bipartite graph 
20121029 

From A student: Suppose that G be a bipartite graph with maximum degree of k.
Prove that:
1)Exists a Kregular bipartite graph that G be subgraph it(H) Answered by Claude Tardif. 





The number of solutions of sinx = x^2 + x +1 
20120901 

From anamika: number of solutions of
sinx = x^2 + x +1
graphically? Answered by Penny Nom. 





Translation of a graph 
20120602 

From Sean: the information is thus:
$f(x)=3(x+1)^22$
I wish to translate up 2 units and move 2 units right. 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. 





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. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You! Answered by Penny Nom. 





Points on a graph 
20110215 

From Maggie: Which set of ordered pairs can be used to graph y = 2x1.
A.(5,9),(1,3),(4,9) B. (2,5),(1,1),(5,9)
C.(2,5),(0,1),(4,3) D. (5,9),(2,3),(4,9)
I cannot figure it out. Could you help me? Answered by Penny Nom. 





The equation of a line 
20101019 

From Sava: I have to write an equation and sketch a graph for the line that meets the given conditions:
A line with slope 15/5 that passes through the point (2.5,4.5) Answered by Penny Nom. 





A taxi ride 
20100922 

From Jack: A taxi ride costs you $2 for the first km and 10 cents for each tenth of a km thereafter.
Sketch a graph of the total cost $C(x) for a ride of xkm, for 0 < x < 2. Hint: The
graph is not smooth.
How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth, Answered by Stephen La Rocque. 





The intersection of two graphs 
20100627 

From Austin: In depth explanation of how to find the intersection points of functions y=4t+300 and y=4.9(t5)^2+300 Answered by Stephen La Rocque. 





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

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





Which values of x satisfy (x2) / (x+4) <7 
20100523 

From Rocco: Which values of x satisfy (x2) / (x+4) <7 Answered by Harley Weston. 





Modelling the roof of a house 
20100323 

From Sandi: This question has been haunting my dreams at night. It states the cross section of the roof of a house is modelled by the function y= 5\12x12+5, where y>0 or y. Now I'm suppose to graph the function. b) Find the slope, height, length of sides, and base of the isosceles triangle. c)Explain what transformation must be applied to the graph of y=x to obtain the graph of y= 5\12x12+5, where y>0 or y=0. 1st I put the equation into my calculator and graphed it. I got 10 for the height. We have had 2 sub teachers this past week. The first one told me the height should be 12 the other one told me 5. So I'm really confused. If I use my 10 units as height and the Pythagorean Theorem I get my sides to be 26 units the base 48 and my slope I calc to be 5/12. Both teachers are pretty sure I'm wrong and they are right but we all have different answers. Please help put this problem to rest so I can rest soundly at night. Thank you for your time. Answered by Penny Nom. 





Sketch the graphs of the following 
20100302 

From musaf: without detailed plotting of points,sketch the graphs of the following
showing relevant information on the graphs:
a) y=(x3)2 +5
b)y=4xx2 Answered by Penny Nom. 





The adjacency matrix of an undirected graph 
20100115 

From Bhavya: Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2 Answered by Robert Dawson. 





Using graphs 
20100104 

From Armstrong: Given that 50 litres of kerosine costs 6000 nira. Draw a graph and read off;
A: The costs of 15 and 34 liters.
B: The number of litres that can be bought for 2300 nira. Answered by Robert Dawson. 





f(x)=x+2sinx 
20091212 

From amroziz: for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Answered by Harley Weston. 





The graph of f(x)=1/x 2 
20091129 

From Kapilan: Please answer the following question:
Sketch the graph of f(x)=1/x 2 Answered by Harley Weston. 





The graph of f(x2) 
20091119 

From Kapilan: Hi please answer the following question:
Given the function f(x)=x^2 sketch the graph of f(x2) Answered by Robert Dawson. 





f(x)= (e^x) / [(e^x)+(ex^2)] 
20091110 

From natalie: I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator.
thanks,
natalie Answered by Chris Fisher and Harley Weston. 





The intersection of two graphs 
20091030 

From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. Answered by Penny Nom. 





Graphing y=(4x^2)^5 
20091025 

From natalie: I want to graph the curve of y=(4x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8.
Thank you so much,
natalie Answered by Harley Weston. 





The intersection of two graphs 
20090902 

From Jaqueline: Find the points of intersection of the graphs of the equations
x^(2 )+ y^2=25 and 2x + y = 10 Answered by Penny Nom. 





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. 





How many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? 
20090527 

From Henry: how many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? Answered by Penny Nom. 





Stairway construction 
20090502 

From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs.
Rule 1: x+y=43 and x+y=46 (cm)
Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length)
I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe.
Did i explain it ok? Thanks for your help.
olivia Answered by Penny Nom. 





The graph of y = 4x^4 
20090407 

From lyric: tell whether the graph opens up or down.write an equation of the axis of symmetry
y=4x^4 Answered by Penny Nom. 





A simple digraph 
20090323 

From Shabkhal: Show that the sum of in degrees of all the nodes of a simple digraph is equal to the sum of out degrees of all its nodes and this sum is equal to the number of edges of the graph. Answered by Victoria West. 





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. 





The graph of y = 6 
20090221 

From Barb: I was given the problem that says "graph the line y = 6" how do I find all the set points that have a y coordinate of 6? I am so lost lost and have no clue how to start. Can you help me please? thanks. Answered by Penny Nom. 





The intersection of two lines 
20090130 

From kaylee: how do you find and graph the intersect of these two equations:
y=2x4 (and) 2y=x
thanks,
kaylee Answered by Stephen La Rocque. 





y = x  4 
20090128 

From tiana: how do you find where to plot Y in a problem that states y=x 4? Answered by Robert Dawson and Penny Nom. 





Graphing a parabola 
20090127 

From Kimberly: I need help with this parabola: graph y=5x^25x6. I am not really understanding how to graph parabolas in general. Can you help me? Answered by Penny Nom. 





Graphing 
20081209 

From Natasha: 2x+y=5 Answered by Robert Dawson. 





Graphing Rational Functions 
20081205 

From Bahra: The question in my homework is: Find all vertical, horizontal, and slant
asymptotes, x and yintercepts, and symetries, and then graph each
function. Check your work with a graphing calculator.
y=3/x+3 meanng: ( y= 3 over x+3) Answered by Janice Cotcher. 





Scaling a logo 
20081020 

From Carl: Hello!
I hope that you can help me out here. I've been trying to figure this out for awhile now and can't come up with the answer logically.
I am a graphic designer by trade and need to figure out how large my client's logo should be.
The logo will need to be sized proportionally with the surface area of the page.
The logo will always be sized at 1.2938(w) x .75(h) on a letter size page (8.5 x 11).
My question is...
When you increase the size of the page (not always proportionally sized  dimensionally) how do figure out the NEW size of the logo.
I could have a page 20" x 40" or 30' x 4'... or ANY size really.
I believe I have the new surface area of the logo but can't find the new dimensions. Answered by Harley Weston. 





Concavity and the second derivative 
20081015 

From Christina: I'm having trouble solving for a second derivative for the following graphing question.
f(x) = (X^2+2x+4)/2x
using the quotient rule, I found:
f'(x) = (x^24)/(2x^2)
however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)(x^24)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3(4x^3 16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3
and making the equation equal to zero result in 0=4 which doesn't seem to make sense... Answered by Penny Nom. 





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. 





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





Graphing Using Double Angle Identities 
20080716 

From Hodan: the Question is:
Describe how you could use your knowledge of Double angle formulas to sketch the graph of each function. Include a sketch with your description.A) F(x)=sin x cos x
B)F(x)=2 cos(squared)x
C) F(x)= tan(x) (divided) by 1tan(squared) x Answered by Janice Cotcher. 





Domain & Range of a Periodic Function 
20080711 

From Michelle: The depth, w metres, of water in a lake can be modelled by the function,
w=5sin(31.5n+63) +12 where n is the number of months since
January 1, 1995. Identify and explain the restrictions on the domain and
range of this function. Answered by Janice Cotcher. 





A point on a graph 
20080708 

From Rita: If (2, b) is a point on the graph of y = (x^2) + 4x, find the value of b. Answered by Leeanne Boehm. 





Points on a graph 
20080703 

From Rita: Dertermine if the given 3 points are on the graph of the equation.
Equation: y = (x^3)  [2(sqrt{x})]
Points: (0, 0); (1, 1); (1, 1) Answered by Penny Nom. 





A piecewise equation 
20080616 

From John: AT&T charges $39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes.
How can I make a piecewise equation of this problem? Answered by Penny Nom. 





The wedges in a circle graph 
20080518 

From Libby: I don't understand how to do this word problem:
The cafeteria workers distributed a survey to the student body asking students to pick 1 from a list of 5 choices for their favorite lunch. The circle graph below gives the results of the survey for the students who responded. What is the measure, in degrees, of the central angle for each choice?
And there is a pie chart that has food choices with these percentages: 25%, 20%, 15%, 10%, and 30% Answered by Leeanne Boehm and Penny Nom. 





Identify the graph 
20080505 

From A parent: Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer.
y = 2x
y = log2x
I can figure out what line on the graph is which equation but unsure what is meant by justify your answer. Answered by Penny Nom. 





How would I graph: x  2 divided by x^2  4? 
20080319 

From Sean: How would I graph: x  2 divided by x^2  4 using a method in extreme values of
functions or completing the square
x  2/ x^24 Answered by Stephen La Rocque. 





Graph the equation P(x)= x^3 + x^2 12x 
20080318 

From Sean: I want to graph the equation : P(x)= x^3 + x^2 12x I was thinking that I would combine
the xvalues, but then I could not use the complete the square technique. Would I have to
just solve the second half of the equation and then graph x^3 seperately Answered by Penny Nom. 





Pythagorean equation 
20080227 

From Judy: X^2 + Y^2 = 5^2
Graph all ordered pairs in the coordiante plane that satisfy the Pythagorean equation, x squared plus y squared equals five squared Answered by Stephen La Rocque. 





How do I graph y = 2x^2? 
20080212 

From Max: How do I graph y=2x^2? Answered by Penny Nom. 





Graphing a parabola 
20080116 

From Sean: How do I find the roots and describe the roots when graphing a parabola?
y =  x^2  4x 3 Answered by Stephen La Rocque. 





Pie graphs 
20080115 

From amarilis: explain why circle graphs are called pie graph or pie charts Answered by Stephen La Rocque. 





Finding the equation of a line from its graph 
20071225 

From ken: I have a graph and it is asking me to find the slope of each line, and
then write its equation. the graph show a negative slope. Would
appreciate the answer if you could show me how to do this question.
Kind regards: Ken Answered by Stephen La Rocque. 





Pictographs 
20071211 

From eniyah: The title of my pictograph is Favorite pets. I have two columns. in my first column is the kind of pet and the second column is the numbers of students, the dogs have 16 student that like them and cats have ten students the likes them. each pictures equals 2 stodents my question is. i have to draw paictures to show the number of students for each row. the key says each symbol equals 2 students. since 16 divided by 2 is 8 can you show me how to make this in a graph Answered by Stephen La Rocque. 





Plotting a function 
20071206 

From Paula: My son has a problem that says plot the point:
2x3y=9
I have explained to him that there must be a function for y in order to plot that point, but he doesn't think so. The question above that one says find the function for y, and I assume we should use that function. Am I wrong? Can we plot a point without a y function. Answered by Stephen La Rocque. 





Two lines 
20071118 

From Kate: represent qraphically the equations of these lines and their intersecting points
xy=2
3x+y=11 Answered by Penny Nom. 





Area of a triangle formed by three points on a graph 
20071026 

From Betty: My question is 'find the are of a triangle whose vertices have
coordinates (3,5),(6,5), and (4,10) Answered by Stephen La Rocque. 





A graph with 100 vertices 
20071024 

From amarjeet: let g be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent only if ij=8 or ij=12. The number of connected components
in g are:
1. 8
2. 12
3. 4
4. 25 Answered by Penny Nom and Victoria West. 





x = y^2 and x = 4 y^2 
20070911 

From Jil: My question is when dealing with parabolas, x=y^2, so that they are sifted on their side you could say,
what will happen to the graph if you change it to x=4y^2. I understand
that the  flips the graph in the other direction but can you simply just plug
in numbers and increase the stretch of the y? Answered by Penny Nom. 





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





Explain how you can shift a parabola up two units 
20070814 

From Marsia: Explain how you can shift a parabola up two units (y axis). Answered by Stephen La Rocque. 





Paying off a loan 
20070808 

From Iona: I borrowed $6000. 00 from a friend to pay school fee.
He said I should not pay back any interest but pay $350.00
monthly after graduation.
(1) Make an equation from the above
(2) make a graph
(3) what is the relationship between the months after graduation and the loan?
(4) what is the horizontal and vertical intercept relate to the problem? Answered by Stephen La Rocque. 





The graph of a log function 
20070730 

From Marsia: How would you describe to another student what the graph of a logarithmic function looks like? Answered by Penny Nom. 





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. 





Parabolas 
20070516 

From Andy: How do you write an equation of a parabola that opens to the left with a vertex of (2,6)? Answered by Stephen La Rocque. 





Finding a parabola's equation by looking at its graph 
20070430 

From Kenzie: The graph shows an arrow going upward crossing at the 2 on the x line
and crossing the 3 on the x line and the vertex on the 6 on the y line. Answered by Stephen La Rocque. 





A sketch of a quadratic equation 
20070414 

From Fee: A ball is thrown upward from the roof of a 25m building. The ball reaches a height of 45m above the ground after 2s and hits the ground 5s after being thrown.
Use the fact that the realtion between the height of the projectile and time is quadratic to draw an accurate graph of the relation on graph paper. Answered by Penny Nom. 





Graphing a line 
20070323 

From mitchell: Graph each equation.
y = 2x + 4 Answered by Jaymi Peterson and Haley Ess. 





A pictograph 
20070314 

From Angie: I am confused! I have to include a title, labels, and a key: Here is the problem
Snickers 45
Kit Kats 65
Nerds 30
Kisses 50
Suckers 75
With the above information please help me make a candy pictograph
I would gladly like your help as my child is a second grader and can not tell me anything about a pictograph Answered by Penny Nom. 





Statistics data 
20070308 

From Parnini: The following table shows the expenditure on different household items by a family. Draw a line graph for the following data: Items : Food Rent Cloth Education Saving Others Expenditure : 2000 2.500 1.500 1.200 4000 3.500 Answered by Stephen La Rocque. 





y = x^2  2 
20070108 

From Mike: Graph the quadratic equation: y=Xsq2 Answered by Penny Nom. 





A linear system 
20070104 

From Harold: System A (4, 2/3) 2x3y=6 and x3y=2
I approached this problem using the addition method.
Could i have found the answer using the graphing method? Answered by Penny Nom. 





y = x  10 
20061103 

From Pam: what is the process for finding the vertex point for an equation such as this, y= x  10. Answered by Penny Nom. 





Plotting a linear equation 
20061009 

From Jennifer:
I am having problems explaining how to do these problems to my child .
graph:2=xy
graph the equation: 2y+x=3
Answered by Penny Nom. 





Find the points of intersection 
20060818 

From Ingrid:
The question says find the points of intersection of the graphs of the equation, and check your results analytically.
x squared + y squared=25
2x+ y=10
Answered by Stephen La Rocque. 





A hamiltonian circuit 
20060724 

From Tom:
1)Prove that every simple not directed graph with 21 vertices and 208 edges has
a hamiltonian circuit but not an Euler circuit.
(I have proved that if we give the 2 edges for each vertices then after a few
steps I have 21 vertices of odd degree and 19 edges.So in the end I have 2
vertices of odd degree.So I have not an Euler circuit.But how can I prove that
there is a Hamiltonian one?)
2)If G is a tree and has a virtex k degree,prove that it also has at least k
vertices degree 1.
Answered by Penny Nom. 





What will the graph of y=x2  2x  3 be? 
20060617 

From Byrony: What will the graph of y=x2  2x  3 be? Answered by Steve La Rocque. 





How do you graph 3x + 6y = 9 by axis intercepts? 
20060522 

From Crystal: How do you graph 3x + 6y = 9 by axis intercepts? Answered by Penny Nom. 





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. 





An epicycloid 
20060410 

From Sharon: What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Answered by Stephen La Rocque and Penny Nom. 





A table of values 
20060328 

From Cindy: Create a table of values for each of the following functions: y=5x, y=52, and y=5x. I dont know to do this. Answered by Stephen La Rocque. 





The graph of y = 2x + 1 
20060223 

From Geneva: I'm having trouble with graphing equations like y=2x+1 which is my homework I'm not sure how to graph it. I'm in the 8th grade taking a 9th grade course algebra I. Answered by Penny Nom. 





Whose photo is he looking at? 
20060219 

From Adeyeri: Looking at a picture a man says, that the father of the person (in photo) is the son of my father. whose photo is he looking at? Answered by Penny Nom. 





Brokenline graphs and histograms 
20060216 

From George:
1. What is the main difference between a brokenline graph and a histogram? Both represent continuous variables.
2. What is the correct way to read a multiplication array: xaxis first and then yaxis, other way around or it doesn't matter?
Answered by Penny Nom. 





Intercepts and slope 
20060115 

From Anthony: Given 1.7x + 0.8y=7.1:
(a) state the intercepts and slope for the graph
(b) Draw the graph Answered by Penny Nom. 





Graphing two lines 
20051120 

From A student: About y = 5x + 24 and y = 3x  8
1. Graph both equations on the same set of axes. When you made your graph, how did you choose the range of x and y values?
2.Find the point of intersection for the graphs.
3. Test the point of intersection you found by substituting its coordinates into the equations. Do the coordinates fit the equations exactly? Answered by Penny Nom. 





Open dots and closed dots 
20050929 

From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny. 





Graphing a linear inequality 
20050826 

From Gina: When graphing a linear inequality, how do you know if the inequality represents the area above the line? Answered by Penny Nom. 





Graphing an inequality 
20050502 

From Janice: I need to know how to graph inequalities. I need to know just abot everything. From graphing an equation to shading. Answered by Leeanne Boehm. 





Graphing inequalities 
20050215 

From Melanie: Solve and Graph the following variable inequalities:
y<2x+4
y>2x+6
3x+4y<24
4x6y>24 Answered by Penny. 





A graph with certain properties 
20041122 

From A student: i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root 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. 





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 commuter 
20040714 

From JJ: A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time.
Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Answered by Penny Nom. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) Answered by Penny Nom. 





The degree sequence of a graph 
20040331 

From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom. 





Graphing lines 
20040208 

From A student: how do you solve y=1\3x+3 and y=1\3x3 by graphing? Answered by Penny Nom. 





Intercepts 
20031104 

From A student: I am totally confused on how to determine intercepts of an equation and then to graph the line. For example, how to determine the intercepts of 2x3y12=0. Answered by Penny Nom. 





Trees 
20031028 

From Ali: Is there any formula for counting the number of trees (graphs)? Answered by Denis Hanson. 





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. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





Functions, graphs and derivatives 
20031005 

From Jathiyah: I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other? Answered by Walter Whiteley. 





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. 





Two intersecting graphs 
20030423 

From Patty:
a) graph the equation x^{2}  y  4 = 0
x^{2} + y^{2} = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places. Answered by Penny Nom. 





y < 2x + 1 
20030301 

From Erika: how can I solve and graph y<2x+1 and which side in the graph should i shade after i finish solving my inequality? 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. 





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. 





Intercepts 
20020904 

From Tamara: Why is it that the x intercept the value of y is 0 and at the y intercept the value of x is 0? Answered by Leeanne Boehm. 





A schedule for a fantasy football league 
20020901 

From Steve: i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 15 = division 1 team 610 = division 2 team 1 should play teams 25 twice and teams 610 once. Answered by Claude Tardif. 





When does an inequality represent the area above the line? 
20020825 

From Tamara: How do you determine that an inequality represents the area above the line and when do you include the line in the solution? Answered by Penny Nom. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. Answered by Penny Nom. 





x and yintercepts 
20020310 

From A student: I have the problem f(x)= ^{X5}/_{X2+X6} and I have to find the vertical asymtope, horizontal asymtope, xintercept, and yintercept. And graph the problem. I am having problems finding the yintercept. Answered by Harley Weston. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





Double bar graphs 
20010909 

From Leslie: My daughter has a homework problem in which she is graphing data from two frequency tables onto a double bar graph. The graph shows how many students worked in a program in two different years, grouped by age. In the first age group, one of the years has no students working, while there were students in that age group in the other year. Answered by Penny Nom. 





Graphing equations 
20010501 

From A student: If, for example, 4x^{2}12x+9=0 and 4x^{2}+12x9=0, which I'm assuming it does since you can derive that equation from the first, why do those two equations have different graphs? Answered by Penny Nom. 





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. 





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

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





Graphing an inequality 
20000802 

From Lori: How do I find x and y and graph this problem 3x + y < 5 Answered by Penny Nom. 





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. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Graphing cube roots 
20000427 

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





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. 





Bar graphs and histograms 
20000111 

From Raeluck: What is the difference between a bar graph and a histogram? Answered by Harley Weston. 





Factoring by graphing 
20000111 

From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom. 





Yintercept 
20000103 

From Kayla Boylan: How do you use and find the yintercept? Answered by Penny Nom. 





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. 





Crossing number 
19991106 

From Christian: The crossing number of a graph G, denoted cr(G) is defined to be the minimum number of (pairwise) crossings of edges among all drawings of the graph in the plane. For example, cr(K5)=1 and cr(K3,3)=1. What is cr(K7,7)? I figured out that the answer is 81. Now I am trying to figure out if K7,7 can be drawn in the plane with less than 81 crossings? I'm not sure how to approach this one. Other than actually drawing it out and checking by trial and error, I am not sure how to approach this problem. Please help! Answered by Denis Hanson. 





A pictograph 
19991028 

From Ali: Please tell me how to make a pictograph.I am 2 grade student. Answered by Penny Nom. 





Broken line graphs 
19991019 

From Lori Samara, Kristi Cameron and the 4th grade students: Students in Ms. Cameron's grade 4 class were wondering if a broken line can be used anywhere in the range on the y  axis when creating a broken line graph? They understand that the broken line can be used at the 0 on the broken line but what if there is a large gap in the data from 100  200? What do we do? The text book and mathematics dictionary do not answer these questions. Answered by Penny Nom. 





Intercepts 
19990924 

From Cassandra: My book says to find where the X and Y intercept, i dont understand who to do this problem. Can you please help here is the problem. it didnt quite explain the instructions. Answered by Penny Nom. 





Stem and Leaf Plot 
19990914 

From Jeanette Sovick: My 5th grade son brought home a math paper, the title of which reads, Reading StemandLeaf Plots...can you explain this so I can explain it to him...There is no book, his teacher just sent this practice sheet home for him to complete and I have no clue! Answered by Penny Nom. 





Graphing a linear equation 
19990527 

From Dylan Bradley: Im in Grade ten and am doing linear equations, I cann't figure out how to make a chart for questions like y = 2x + 3 Answered by Penny Nom. 





Dotted graph paper 
19990408 

From Bridget Winward: A teacher at our school is trying to locate dotted graph paper online or in print. His class would like to make three dimensional, geometerical drawings. Please let us know if you have a good source. Answered by Jack LeSage. 





Graphing the Derivative 
19990118 

From Milena Ghebre: This question has been nagging me for sometime now. Is there a way of finding out the derivative of a function, just by looking at the graph of it? Answered by Walter Whiteley. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





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. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





Graph Distortion 
19980219 

From Dana Steffan: What exactly is graph distortion? I have to explain it for a project and I can't seem to find anything on it. Answered by Penny Nom. 





The twodigit numbers from 1099 
19980121 

From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a twodigit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the twodigit numbers from 1099? Please help and thank you for any assistance you can give me. Answered by Penny Nom. 





Quadratic Graphs 
19980113 

From Simon Batten: How does varying the values a,b and c affect the graph of y=ax^{2} + bx + c? Answered by Harley Weston. 





(2)^x 
19971212 

From Ken Bokinac: During our math class last week we came accross an equation that we could not graph we were wondering if you could help us try and graph it. The question is: y=(2)^x Answered by Harley Weston. 





Graphing Inequalities of Conic Sections 
19970324 

From James Sheldon: I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade: x^2+y^2 is greater than or equal to 16 xy > 4 So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it... Answered by Penny Nom. 





Where do 2^x and x^2 intersect? 
19960723 

From Darin M Selfridge: The intersecting points of y=2^x and y=x^2, graphed along with x^2=2^x, are obviously three... (2,4), (4,16) and (?,?). I am having problems figuring out the value, and even an equation for the (?,?). Can you help? Answered by Harley Weston Chris Fisher. 





How do you graph these inequalities? 
19960517 

From Robert: How do you graph the inequalities 5+gg, and g+h>6 on one coordinate plane? Answered by Harley Weston and Maxine Stinka. 





How do you graph these equations? 
19960430 

From David Gamble: How do you graph the equation x=3 on a x,y graph? Also how do you graph f(x)=3x + 2 on the same graph? Answered by Harley Weston and Maxine Stinka. 





l'équation d'une rotation dans un graphique cartésien 
20011114 

From Ghaith: je d6sir que vous me rafraichissez un peu la mémoire s.v.p. j'aimerai savoir l'équation d'une rotation dans un graphique cartésien merci Answered by Claude Tardif. 





la pantographie 
19991118 

From Erick et Christine: Nous recherchons la définition de pantographie voltaïque, que représente cette "figure" ? estce qu'on peut en définir une unité de mesure ? Answered by Claude Tardif. 

