Chapter 1, Problem 7CR

To determine

To write: A function $g$ whose graph represents the indicated transformations of graph of $f$ .

Answer to Problem 7CR

Graph that represents the indicated transformations of graph of $f$ is $g(x)=-\left|x+4\right|$ .

Explanation of Solution

Given information: The given function is $f(x)=\left|x\right|$ ;reflection to the $x-\mathrm{axis}$ followed by a translation $4$ units to the left.

Calculation:The given function is $f(x)=\left|x\right|$ .

Multiply output by $-1$ to reflect over the $x-\mathrm{axis}$ .

  $g(x)=-\left|x\right|$ .

Add 4 to input to translate $4$ units to the left.

  $g(x)=-\left|x+4\right|$ .

Graph of function and parent function is: