+0

0
110
8
+222

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

Apr 16, 2021

#1
+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
+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 understand

Apr 16, 2021
#3
+222
0

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

CPhilFanboy  Apr 16, 2021
#4
+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
+222
+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
+180
+1

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

Mathdory  Apr 16, 2021
#8
0

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

Guest Apr 16, 2021
#7
+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