Chapter 1.2, Problem 3Q

To determine

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

Answer to Problem 3Q

Parent function is $f(x)=\left|x\right|$ , $g$ is translated $1$ unit left and $2$ units down.

Explanation of Solution

Given information: Function is $g(x)=\left|x+1\right|-2$ .

Calculation:

  $g$ belongs to family of absolute value functions,

Parent function is $\left|x\right|$ .

  

Red line represents the given function whereas blue line represents parent function.

Given function is translated $1$ unit left and $2$ units down with respect to the parent function.

Domain of parent function: All real numbers

Range of parent function: $y\ge 0$

Domain of given function: All real numbers

Range of given function: $y\ge -2$

Thus, parent function is $f(x)=\left|x\right|$ , $g$ is translated $1$ unit left and $2$ units down.