+0  
 
0
55
8
avatar+210 

Please do your best to explain since I want to learn how to do this as well.

 Apr 16, 2021
 #1
avatar+180 
+1

(b): 

 

Take a point (a,b)  on the graph of y=f(x), so b=f(a). Since \(\left( 3a - 1, \frac{b}{2} \right)\) lies on the graph of y=g(x) we have that \(\frac{b}{2} = g(3a - 1). \)

 

Substituting b=f(a) we get \(\frac{f(a)}{2} = g(3a - 1).\)

In order to express g(x) in terms of f(x) we can let x = 3a-1 Then a=\(\frac{x + 1}{3}\), so

 

 

                                                       \(g(x) = \frac{f(a)}{2} = \frac{1}{2} f \left( \frac{x + 1}{3} \right).\)

 Apr 16, 2021
 #2
avatar+180 
+1

Sorry that I can't do the problems (a) and (c) because the LaTeX code is too complicated for drawing the diagram. I hope you understandfrown

 Apr 16, 2021
 #3
avatar+210 
0

It's okay, I understand, can anyone else help? It's due tomorrow for me.

CPhilFanboy  Apr 16, 2021
 #4
avatar+180 
+1

This link might help a bit

 

https://web2.0calc.com/questions/help-pls-due-today-help-needed-asap

Mathdory  Apr 16, 2021
 #5
avatar+210 
+1

Yeah... I looked at that one, I wasn't able to understand what they are saying though, thanks for the help!

CPhilFanboy  Apr 16, 2021
 #6
avatar+180 
+1

Ok, if i can get the diagram working, I might be able to answer the questions.

Mathdory  Apr 16, 2021
 #8
avatar
0

It is a ASY, so the latex won't work

Guest Apr 16, 2021
 #7
avatar+180 
+2

First, we observe that the graph of y=f(x) consists of line segments, connecting the points (-4, 4), (-1,0), (0,2),  and (4,-4).

 

 

So to plot the graph of y=g(x) we can apply the transformation  \((a,b) \to \left( 3a - 1, \frac{b}{2} \right)\) to each of these points, and then connect them. This gives us the points (-13,2), (-4,0), (-1,1), and (11,-2).  

 

 Hope this helps! 

 

I got it working.

 Apr 16, 2021

76 Online Users

avatar
avatar
avatar
avatar