# What is the domain and range of y = -7 /(x-5)?

Aug 11, 2015

Domain: $\left(- \infty , 5\right) \cup \left(5 , + \infty\right)$
Range: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

#### Explanation:

The function is defined for all real numbers except for any value of $x$ that makes the denominator equal to zero.

In your case, $x$ can take any value except

$x - 5 \ne 0 \implies x \ne 5$

The domain of the function will thus be $\mathbb{R} - \left\{5\right\}$, or $\left(- \infty , 5\right) \cup \left(5 , + \infty\right)$.

In order to determine the range of the function, you need to take into account the fact that this fraction cannot be equal to zero, since the numerator is constant.

This means that the range of the function will be $\mathbb{R} - \left\{0\right\}$, or $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

graph{-7/(x-5) [-10, 10, -5, 5]}