Chapter 5.8, Problem 15P

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

left $\frac{1}{2}$ unit

To determine

What will be the equation when the translation of $y=\left|x\right|$ is $\frac{1}{2}$ units left.

Answer to Problem 15P

The equation is $y=\left|x+\frac{1}{2}\right|$ .

Explanation of Solution

Given information:

The given translation is $\frac{1}{2}$ units left.

Calculation:

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

When the translation is $\frac{1}{2}$ units left, then the equation becomes $y=\left|x+\frac{1}{2}\right|$ .

So, each point of $y=\left|x+\frac{1}{2}\right|$ , is $\frac{1}{2}$ units left than the corresponding points of $y=\left|x\right|$ .

The graph of the equation is:

  

Hence, the equation is $y=\left|x+\frac{1}{2}\right|$ .