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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 vertically by a factor of $4.$

 

Any help is appreciated. Thanks so much!

 Jun 21, 2021
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(a) See the graph below.

 

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

 

(c) We stretch the graph horiztonally by a factor of 3, then stretch the graph vertically by a factor of 1/2, then shift down 3 units.

 

 Jun 23, 2021

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