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The graph of y = f(x) is shown below. 

 

Graph of y=f(x)

 

For each point (a,b) that is on the graph of y = f(x), the point \(\left( 3a - 1, \frac{b}{2} \right)\)is plotted, forming the graph of another function y = g(x). As an example, the point (0,2) lies on the graph of y = f(x), so the point \((3 \cdot 0 - 1, 2/2) = (-1,1)\) lies on the graph of y = g(x).

 

(a) Plot the graph of y = g(x). Include the diagram as part of your solution.

 

(b) Express $g(x)$ in terms of $f(x).$

 

(c) Describe the transformations that can be applied to the graph of y = f(x) to obtain the graph of y = g(x). For example, one transformation could be to stretch the graph vertically by a factor of 4.

 

 

PLEASE HELP!!! A thorough explanation would be appreciated since I am super confused and want to learn how to do this problem and other similar types of problems!!! Thank you so much!!!

 Nov 8, 2020
 #1
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(a) See the graph below.

 

(b) g(x) = 1/3*f(2x + 2).

 

(c) We stretch the graph horiztonally by a factor of 2, then stretch the graph vertically by a factor of 3, then shift down 2 units.

 

 Nov 8, 2020
 #2
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Hi! Thanks for your answer! Would you be able to explain how you got your answer for part (b)? How did you arrive at that answer? If I understand that, I know how you arrive at your other answers! Thank you so much!!!  

Guest Nov 9, 2020

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