# What is the domain and range of  y = (-4) / ( sqrt (x +1))?

Jun 19, 2018

The domain is $x \in \left(- 1 , + \infty\right)$.
The range is $y \in \left(- \infty , {0}^{-}\right)$

#### Explanation:

The function is

$y = - \frac{4}{\sqrt{x + 1}}$

What's under the square root sign is $\ge 0$ and also, the denominator $\ne 0$

Therefore,

$x + 1 > 0$

$\implies$, $x > - 1$

The domain is $x \in \left(- 1 , + \infty\right)$

When $x \to - {1}^{+}$, $\implies$, $y \to - \infty$

When $x \to + \infty$, $\implies$, $y \to {0}^{-}$

The range is $y \in \left(- \infty , {0}^{-}\right)$

graph{-4/sqrt(x+1) [-7.1, 28.93, -12.47, 5.55]}