Chapter 0.2, Problem 8QR

To determine

To describe: How the graph of $f$ can be transformed to the graph of $g$ .

Answer to Problem 8QR

The function $f\left(x\right)=\left|x\right|$ is translated $5$ units to the right, $2$ unit to the up to the graph of $g\left(x\right)$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=\left|x\right|,g\left(x\right)=\left|x-5\right|+2$ .

Calculation:

The given function is $f\left(x\right)=\left|x\right|,g\left(x\right)=\left|x-5\right|+2$ .

The graph of the given function $f\left(x\right)=\left|x\right|$ is below:

  

The given function is $g\left(x\right)=\left|x-5\right|+2$ .

Compare $g\left(x\right)=\left|x-5\right|+2$ with the general form $y=a\left|x-h\right|+k$ :

  $a=1,h=5,k=2$

The vertex $\left(h,k\right)$ is $\left(5,2\right)$ .

The axis of symmetry is $x=5$ .

The function $f\left(x\right)=\left|x\right|$ is translated $5$ units to the right, $2$ unit to the up.

Now, draw the graph of the function $f\left(x\right)$ is below: