# What is the range of the function y=-3/(4x+4)?

Jun 8, 2017

$y \in \mathbb{R} , y \ne 0$

#### Explanation:

$\text{rearrange making x the subject}$

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

$\Rightarrow y \left(4 x + 4\right) = - 3 \leftarrow \textcolor{b l u e}{\text{cross-multiplying}}$

$\Rightarrow 4 x y + 4 y = - 3 \leftarrow \text{ distributing}$

$\Rightarrow 4 x y = - 3 - 4 y$

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

$\text{the denominator cannot equal zero as this would make}$
$\text{the function undefined}$
$\text{equating the denominator to zero and solving gives the}$
$\text{value that y cannot be}$

$\text{solve "4y=0rArry=0larrcolor(red)" excluded value}$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$