Chapter 1.1, Problem 3E

To determine

To identify: The family to which $f$ belongs and then to compare the graph of $f$ to graph of its parent function.

Answer to Problem 3E

  $f$ belongs to the family of absolute-value functions.

Explanation of Solution

Given information: Graph of function $f(x)=2\left|x+2\right|-8$ .

As the graph is V-shaped, $f$ belongs to the family of absolute-value functions.

Graph of parent absolute value function is like:

  

Comparing given function with parent function $g(x)=\left|x\right|$ ,

the given graph is shifted down vertically by $8units$ and by $2units$ to the left horizontally and it is also narrower with respect to the parent absolute value function. The domain of the given function is all real numbers while range is $y\ge -8$ , whereas range of parent function is $y\ge 0$ .