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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 $\left( 3a - 1, \frac{b}{2} \right)$ 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 

 Oct 15, 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.

 

 Oct 15, 2022

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