How do you find the domain and range of y=abs(x+4)?

Jun 5, 2017

Domain; $\left(- \infty , + \infty\right)$
Range: $\left[0 , + \infty\right)$

Explanation:

$y = \left\mid x + 4 \right\mid$

$y$ is defined $\forall x \in \mathbb{R}$

Hence the domain of y is $\left(- \infty , + \infty\right)$

$y \ge 0 \forall x \in \mathbb{R}$

Thus, the range of $y$ is $\left[0 , + \infty\right)$

This can be seen by the graph of $y$ below.

graph{abs(x+4) [-14.16, 11.16, -3.82, 8.84]}