# What is the domain and range of f(x) = (4x^2 - 4x - 8) / (2x + 2)?

Jun 18, 2018

The domain is $x \in \mathbb{R}$.
The range is $y \in \mathbb{R}$

#### Explanation:

The function is

$f \left(x\right) = \frac{4 {x}^{2} - 4 x - 8}{2 x + 2} = \frac{4 \left({x}^{2} - x - 2\right)}{2 \left(x + 1\right)} = \frac{2 \left(x - 2\right) \cancel{x + 1}}{\cancel{x + 1}}$

$= 2 \left(x - 2\right)$

This is the equation of a line, $y = 2 x - 4$

The domain is $x \in \mathbb{R}$

The range is $y \in \mathbb{R}$

graph{(4x^2-4x-8)/(2x+2) [-18.02, 18.02, -9.01, 9.02]}