# How do you find the domain and range of y=5/(x-1)?

Dec 24, 2016

The domain is $= \mathbb{R} - \left\{1\right\}$
The range is $= \mathbb{R} - \left\{0\right\}$

#### Explanation:

As you cannot divide by $0$, $\implies$, $x \ne 1$

Therefore,

The domain of $x$ is ${D}_{x} = \mathbb{R} - \left\{1\right\}$

The limit of $y$ as $x \to \infty$ is

${\lim}_{x \to - \infty} y = {\lim}_{x \to - \infty} \frac{5}{x} = {0}^{-}$

${\lim}_{x \to + \infty} y = {\lim}_{x \to + \infty} \frac{5}{x} = {0}^{+}$

There is a horizontal asymptote at $y = 0$

Therefore,

The range is ${R}_{y} = \mathbb{R} - \left\{0\right\}$