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Graphing piecewise functions 2014-03-29
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!

Answered by Penny Nom.
What does y= f(x) actually mean? 2013-12-31
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:


What does y= f(x) actually mean?

Answered by Penny Nom.
Solve sin 3x = -0.1254 with x between o and 360 degrees 2013-02-21
From David:
sin 3x = -0.1254 0
Answered by Harley Weston.
Solve sin 3x = -0.1254 with 0 2013-02-21
From David:
sin 3x = -0.1254 0
Answered by Harley Weston.
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.
Linear inequalities 2011-03-25
From Alice:
OK. I'm in algebra 1 and the linear inequality is
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.
Modelling the roof of a house 2010-03-23
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\12|x-12|+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\12|x-12|+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.
Using graphs 2010-01-04
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.
y=2x+1 and y=2x-1 2009-08-28
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.
Graph 2x-3y+15=0 2009-08-20
From Diem:
Graph 2x-3y+15=0
Answered by Leeanne Boehm.
Stairway construction 2009-05-02
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.
Graphing 2008-12-09
From Natasha:
Answered by Robert Dawson.
Scaling a logo 2008-10-20
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 2008-10-15
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^2-4)/(2x^2)

however, using the quotient rule again I can't seem to solve it (concavity):
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4

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 2008-08-12
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 2008-08-01
From James:
Question from james, a student:


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 2008-07-16
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 1-tan(squared) x
Answered by Janice Cotcher.
Domain & Range of a Periodic Function 2008-07-11
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.
Plotting a function 2007-12-06
From Paula:
My son has a problem that says plot the point: 2x-3y=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.
x = y^2 and x = -4 y^2 2007-09-11
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.
Explain how you can shift a parabola up two units 2007-08-14
From Marsia:
Explain how you can shift a parabola up two units (y axis).
Answered by Stephen La Rocque.
Circumscribing a golden cuboid with a sphere: surface areas 2007-06-14
From Ainslie:
A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi.

Answered by Stephen La Rocque.
Finding a parabola's equation by looking at its graph 2007-04-30
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 linear system 2007-01-04
From Harold:
System A (4, 2/3)
2x-3y=6 and x-3y=2

I approached this problem using the addition method.

Could i have found the answer using the graphing method?

Answered by Penny Nom.
The graph of y = 2x + 1 2006-02-23
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.
Open dots and closed dots 2005-09-29
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 2005-08-26
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 2005-05-02
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.
Perfecting an ideal gambling system 2005-03-06
From Gaz:
I am a screenwriter, currently in the fortunate position of having the development of a Screenplay funded by the South Australian Film Corporation. The (anti)hero of this screenplay is a statistician whose life is falling apart around him, thanks in part to his obsession with perfecting an "ideal" gambling system.
Answered by Andrei Volodin.
Graphing inequalities 2005-02-15
From Melanie:
Solve and Graph the following variable inequalities:





Answered by Penny.
Graphing lines 2004-02-08
From A student:
how do you solve y=1\3x+3 and y=1\3x-3 by graphing?
Answered by Penny Nom.
Intercepts 2003-11-04
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 2x-3y-12=0.
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.
Graphing equations 2001-05-01
From A student:
If, for example, 4x2-12x+9=0 and -4x2+12x-9=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.
Graphing F(x) = 3x 2000-11-06
From Jose:
graph the exponential problem F(x)=3x
Answered by Harley Weston.
Graphing an inequality 2000-08-02
From Lori:
How do I find x and y and graph this problem

3x + y < 5

Answered by Penny Nom.
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.
A matrix equation 2000-05-14
From A student:
Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphing-calculators: 2a+3b-4c+d=20

Answered by Penny Nom.
Graphing cube roots 2000-04-27
From Heather Jones:
What do the graphs of cube roots look like?
Answered by Walter Whiteley.
Factoring by graphing 2000-01-11
From Dylan Kirkwood:
How can you factor a quadratic equation by graphing it?
Answered by Penny Nom.
Fibonacci Numbers 1999-12-15
From Gary Nelb:
I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different.
Answered by Denis Hanson.
Stem and Leaf Plot 1999-09-14
From Jeanette Sovick:
My 5th grade son brought home a math paper, the title of which reads, Reading Stem-and-Leaf 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 1999-05-27
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.
Graphing the Derivative 1999-01-18
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.

Intersection of planes 1998-11-22
From Dave Rasmussen:
I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Co-ordinate 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.
Graphing Inequalities of Conic Sections 1997-03-24
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.

How do you graph these inequalities? 1996-05-17
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? 1996-04-30
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 2001-11-14
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.
isomorphisme 2000-08-10
From Romain Kroes:
Pour les beoins d'un ouvrage d'économie que je suis en train de terminer, pouvez-vous me dire qui est (sont) l'inventeur de l' "isomorphisme" en mathématiques (calcul tensoriel)?
Answered by Claude Tardif.
la pantographie 1999-11-18
From Erick et Christine:
Nous recherchons la définition de pantographie voltaïque, que représente cette "figure" ? est-ce qu'on peut en définir une unité de mesure ?
Answered by Claude Tardif.



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