# What is the domain and range of y = 1/(x - 2)?

Mar 10, 2018

Domain: $\left(- \infty , + 2\right) \cup \left(+ 2 , + \infty\right)$
Range: $\left(- \infty , + \infty\right)$

#### Explanation:

$y = \frac{1}{x - 2}$

$y$ is defined for all $x \in \mathbb{R} : x \ne + 2$

Hence, The domain of $y$ is $\left(- \infty , + 2\right) \cup \left(+ 2 , + \infty\right)$

Consider:

${\lim}_{x \to {2}^{+}} y = + \infty$ and ${\lim}_{x \to {2}^{-}} y = - \infty$

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

As can be deduced from the graphic of $f \left(x\right)$ below:

graph{1/(x-2) [-16.01, 16.02, -8.01, 8]}