# How do you find the domain and range of y= 1 / (x-3)?

Jun 13, 2016

Domain $= \left\{x : x \epsilon \mathbb{R} , x \ne 3\right\}$
Range $y = \left\{y : y \epsilon \mathbb{R} , y \ne 0\right\}$

#### Explanation:

The domain is the set of all the x-values.

We notice that $x$ is in the denominator, and the only restriction for a denominator is that it may not be equal to 0.
If $x - 3 = 0 \Rightarrow x = 3$

So $x$ can have any value except 3.

This equation can also be written as $\left(x - 3\right) = \frac{1}{y}$
The range is the set of all the $y$ values

In this case we can see that $y$ may not be equal to 0

So $y$ can have any value except 0.

Domain $= \left\{x : x \epsilon \mathbb{R} , x \ne 3\right\}$
Range $y = \left\{y : y \epsilon \mathbb{R} , y \ne 0\right\}$