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

Jul 9, 2017

Domain: $x \in \mathbb{R} | x \ne 4$, in interval notation: $\left(- \infty , 4\right) \cup \left(4 , \infty\right)$
Range : $y \in \mathbb{R}$ , in interval notation: $\left(- \infty , \infty\right)$

Explanation:

$y = \frac{x \left(x - 3\right)}{x - 4}$

Domain: Denominator is undefined at $0 \therefore x - 4 \ne 0 \mathmr{and} x \ne 4$

Domain: $x$ may be any real number except $4 \therefore x \in \mathbb{R} | x \ne 4$

In interval notation: $\left(- \infty , 4\right) \cup \left(4 , \infty\right)$

Range : Any real number i.e $y \in \mathbb{R}$

In interval notation: $\left(- \infty , \infty\right)$

graph{(x(x-3))/(x-4) [-640, 640, -320, 320]}