Chapter 5.8, Problem 16P

Write an equation for each translation of $y=\left|x\right|$.

right $\frac{2}{3}$ unit

To determine

What will be the equation when the translation of $y=\left|x\right|$ is $\frac{2}{3}$ units right.

Answer to Problem 16P

The equation is $y=\left|x-\frac{2}{3}\right|$ .

Explanation of Solution

Given information:

The given translation is $\frac{2}{3}$ units right

Calculation:

Consider the equation $y=\left|x\right|$ .

When the translation is $\frac{2}{3}$ units right, then the equation becomes $y=\left|x-\frac{2}{3}\right|$ .

So, each point of $y=\left|x-\frac{2}{3}\right|$ , is $\frac{2}{3}$ units right than the corresponding points of $y=\left|x\right|$ .

The graph of the equation is:

  

Hence, the equation is $y=\left|x-\frac{2}{3}\right|$ .