# What is the domain and range of y=absx -2?

The domain is the set of real numbers R

For the range we note that

$y + 2 = | x | \ge 0 \implies y \ge - 2$

Hence the range is the set $\left[- 2 , + \infty\right)$

May 6, 2018

Domain: $\left\{x \in \mathbb{R}\right\}$
Range: $y = \left[- 2 , {\infty}^{+}\right)$

#### Explanation:

The domain, in words is x is a real number, and the range is y
is greater than or equal to -2
.

graph{|x|-2 [-10, 10, -5.21, 5.21]}

Absolute values are always positive numbers, since they express the distance a number is from zero, which seems pretty useless at first, but they are nice in instances such as chemistry, or physics, where you want to calculate percentage error.

$y = | x | - 2$ is like $y = x - 2$, but all the $y$ values must be greater than or equal to $- 2$

Hope that helps!