Chapter 1.2, Problem 8QR

To determine

Toexplain:The transformation of the graph of $f\left(x\right)=\left|x\right|$ to the graph of $g\left(x\right)=\left|x-5\right|+2$ .

Answer to Problem 8QR

Shift the graph of $f\left(x\right)=\left|x\right|$ five units to the right and two units upwards to get the graph of $g\left(x\right)=\left|x-5\right|+2$ .

Explanation of Solution

Given information:The functions are $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\left|x-5\right|+2$ .

Consider a function $f\left(x\right)$ . Shift the graph of $f\left(x\right)$ to the right by $k$ units to draw the graph of $f\left(x-k\right)$ and shift $f\left(x\right)$ to upwards by $k$ units to draw the graph of $f\left(x\right)+k$ .

The given functions are $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\left|x-5\right|+2$ .First draw the graph of $f\left(x\right)=\left|x\right|$ . Now, shift the graph of $f\left(x\right)=\left|x\right|$ five units to the right and, then two units upwards.

Therefore, shift the graph of $f\left(x\right)=\left|x\right|$ five units to the right and two units upwards to get the graph of $g\left(x\right)=\left|x-5\right|+2$ .