Chapter 1.1, Problem 24E

To determine

To graph: The given function and its parent function and then to describe the transformation.

Answer to Problem 24E

The graph of $g(x)=\frac{4}{3}x$ is a vertical stretch by a factor of $\frac{4}{3}$ , with respect to the graph of the parent linear function.

Explanation of Solution

Given information: Given function is $g(x)=\frac{4}{3}x$ .

Graph:

The function $g$ is a linear function. Using a table of values to graph the given function and the parent function $f(x)=x$ ,

  $\begin{array}{lll}x\hfill & f(x)=x\hfill & g(x)=\frac{4}{3}x\hfill \\ -2\hfill & -2\hfill & -\frac{8}{3}\hfill \\ -1\hfill & -1\hfill & -\frac{4}{3}\hfill \\ 0\hfill & 0\hfill & 0\hfill \\ 1\hfill & 1\hfill & \frac{4}{3}\hfill \\ 2\hfill & 2\hfill & \frac{8}{3}\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $g$ (shown by blue colored line) is a vertical stretch by a factor of $\frac{4}{3}$ w.r.t. the graph of the parent linear function $f(x)=x$ (shown by green colored line).

So, the graph of $g(x)=\frac{4}{3}x$ is a vertical stretch by a factor of $\frac{4}{3}$ , with respect to the graph of the parent linear function.