# How do you write # y= |x-5| -4# as a piecewise function?

##### 2 Answers

Start with the piecewise definition of the absolute value function:

Substitute

Simplify the inequalities:

Distribute the -1:

Make two separate equation of the original:

Simplify:

#### Explanation:

First let's look at the graph or the original function

The left half of the graph where

Using the slope intercept form of a line

The right half of the graph where

Using the slope intercept form of the line

Written in piecewise form

Note that I arbitrarily assigned