# What is the domain and range of Y(x)= -2 sqrt(-x) + 20?

Oct 3, 2016

Domain: $\left(- \infty , 0\right) : x \in \mathbb{R}$
Range: $\left(- \infty , 20\right) : Y \left(x\right) \in \mathbb{R}$

#### Explanation:

$Y \left(x\right) = - 2 \sqrt{- x} + 20$

Assume $Y \left(x\right) \in \mathbb{R} \to x \le 0 : x \in \mathbb{R}$

Hence domain of $Y \left(x\right)$ is $\left(- \infty , 0\right)$

Since the coefficient of the radical is negative $\left(- 2\right)$, $Y \left(x\right)$ has a greatest value of $20$ at $x = 0$. $Y \left(x\right)$ has no finite least value.

Hence the range of $Y \left(x\right)$ is $\left(- \infty , 20\right)$