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The graph of y=f(x) is shown below:
 

 

For each point (a,b)  that is on the graph of y=f(x), the point (3a-1,b/2)  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*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. 
 

 Aug 21, 2021
edited by Guest  Aug 21, 2021
 #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.

 

 Aug 21, 2021
 #2
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Thank you so much for the answer, lifesaver! But can someone show me how you got there?

Guest Aug 23, 2021

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