# How do you find the domain and range of  y = -sqrt(x+6)+7 ?

Jun 19, 2018

#### Answer:

The domain is $x \in \left[- 6 , + \infty\right]$. The range is $y \in \left(- \infty , 7\right]$

#### Explanation:

The function is

$y = - \sqrt{x + 6} + 7$

What's under the square root sign must be $\ge 0$

Therefore,

$x + 6 \ge 0$

$\implies$, $x \ge - 6$

The domain is $x \in \left[- 6 , + \infty\right]$

When $x = - 6$

$y = - \sqrt{- 6 + 6} + 7 = 0 + 7 = 7$

And when $x \to + \infty$

$y \to \left(- \sqrt{+ \infty + 6} + 7\right) = - \infty$

The range is $y \in \left(- \infty , 7\right]$

graph{-sqrt(x+6)+7 [-32.17, 71.9, -28.34, 23.65]}