# How do you find the domain and range of y=5/(x-3)?

Jun 6, 2018

The domain is $x \in \left(- \infty , 3\right) \cup \left(3 , + \infty\right)$. The range is $y \in \left(- \infty , 0\right) \cup \left(0 , \infty\right)$.

#### Explanation:

The denominator must be $\ne 0$.

Therefore,

$x - 3 \ne 0$

$\implies$, $x \ne 3$

The domain is $x \in \left(- \infty , 3\right) \cup \left(3 , + \infty\right)$

To calculate the range, proceed as follows :

Let $y = \frac{5}{x - 3}$

$y \left(x - 3\right) = 5$

$y x - 3 y = 5$

$x y = 5 + 3 y$

$x = \frac{5 + 3 y}{y}$

The denominator must be $\ne 0$.

$y \ne 0$

The range is $y \in \left(- \infty , 0\right) \cup \left(0 , \infty\right)$

graph{5/(x-3) [-52, 52.03, -26, 26.03]}