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

Oct 2, 2017

Domain $\left\{x \in \mathbb{R}\right\}$
Range $\left\{y \in \mathbb{R} | 0 < y < \infty\right\}$

#### Explanation:

Since $f \left(x\right) = - | x + 4 |$ is a continuous function there are no restrictions on $x$ so domain is:

$\left\{x \in \mathbb{R}\right\}$

Maximum value of the function is $0$ this occurs when $x = - 4$.
Because the value in absolute bars is always positive, the minimum value will be $- \infty$

So range is;

$\left\{y \in \mathbb{R} | - \infty < y \le 0\right\}$