# How do you find the domain and range of y=-3/(4x+4) ?

Jun 8, 2017

Domain: $\left(- \infty , - 1\right) \cup \left(- 1 , + \infty\right)$
Range: $\left(- \infty , + \infty\right)$

#### Explanation:

$y = - \frac{3}{4 x + 4}$

$y$ is defined for all real x except where $4 x + 4 = 0$
i.e where $x = - 1$

$\therefore y$ is defined $\forall x \in \mathbb{R} : x \ne - 1$

Hence the domain of $y$ is $\left(- \infty , - 1\right) \cup \left(- 1 , + \infty\right)$

$L i {m}_{\text{x->-1 (-)}} y = + \infty$

and

$L i {m}_{\text{x->-1 (+)}} y = - \infty$

Hence the range of $y$ is $\left(- \infty , + \infty\right)$

This can be seen by the graph of $y$ below.
graph{-3/(4x+4) [-10, 10, -5, 5]}