# What is the domain and range of y=-abs(x-5)?

Jul 6, 2018

There is no restriction on $x$, so the domain is $- \infty < x < + \infty$

#### Explanation:

Range:
The absolute bars mean that $| x - 5 |$ cannot be negative, so the function with the extra minus outside the bars cannot be positive.
$- \infty < y \le 0$
Maximum value will be reached at $\left(5 , 0\right)$
graph{-|x-5| [-3.88, 16.12, -7.64, 2.36]}