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

D: $x \in \mathbb{R}$; R: $y \le 0$

#### Explanation:

Domain - the list of all permissible $x$ values

There are no values of x that are impermissible and so the domain of $x$ is all real numbers, which we can write in a number of ways, with one way being

$x \in \mathbb{R}$

Range - the list of all resulting $y$ values

When we evaluate an absolute value, we will always get a value that is at least 0. In our current question, when x=-4, abs(-4+4)=0; x=-5 and x=-3 returns 1, and so forth.

So we have a positive number coming from the absolute value brackets to which we are multiplying a $- 1$, which will make the values negative. And so the possible values of $y$ start at 0 and decrease towards $- \infty$. We can write that as:

$y \le 0$