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# Functions

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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