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The graph of y = f(x) is shown below.

 

I cannot seem to upload a file so, I will try my bes to describe the graph.

The graph is composed of 3 lines. Where the first line starts at $(-4, 4)$ and ends at $(-1, 0)$. While the second and third lines start at $(-1, 0),$ $(0, 2),$ and ends at $(0, 2), $ $(4, -4),$ respectively.


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 (-1, 1) lies on the graph of y = g(x).

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

 

(b) 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.

 Jul 26, 2022
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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.

 

 Jul 26, 2022

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