# Question #bcc54

Feb 5, 2018

Domain: $x \in \mathbb{R}$
Range: $y \le 8$

#### Explanation:

The domain is all real numbers because there is no value of $x$ that cannot be substituted.

$f \left(x\right)$ is a transformation of $y = {x}^{2}$, which has a natural range of $y \ge 0$.

To get $f \left(x\right)$ we reflect over the $x$-axis and then translate ${x}^{2}$ down 8 units, which changes the range to $y \le 8$.