Chapter 1.1, Problem 29E

To determine

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

Answer to Problem 29E

The graph of $h(x)=-3\left|x\right|-1$ is a vertical stretch by a factor of $3$ and reflection over $x-axis$ and vertical translation of $1unit$ downward with respect to the graph of the parent absolute value function.

Explanation of Solution

Given information: Given function is $h(x)=-3\left|x\right|-1$ .

Graph:

The function $h$ is an absolute value function. Using a table of values to graph the given function and the parent function $g(x)=\left|x\right|$ ,

  $\begin{array}{lll}x\hfill & g(x)=\left|x\right|\hfill & h(x)=-3\left|x\right|-1\hfill \\ -2\hfill & 2\hfill & -7\hfill \\ -1\hfill & 1\hfill & -4\hfill \\ 0\hfill & 0\hfill & 0\hfill \\ 1\hfill & 1\hfill & -4\hfill \\ 2\hfill & 2\hfill & -7\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $h$ (shown by blue colored line) is a vertical stretch by a factor of $3$ and reflection over $x-axis$ and vertical translation of $1unit$ downward w.r.t. the graph of the parent absolute value function $g(x)=\left|x\right|$ (shown by green colored line).

So, the graph of $h(x)=-3\left|x\right|-1$ is a vertical stretch by a factor of $3$ and reflection over $x-axis$ and vertical translation of $1unit$ downward with respect to the graph of the parent absolute value function.