# How do you find the domain and range of f(x) = 7/(x+3)?

May 1, 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:

Let $y = \frac{7}{x + 3}$

The denominator is $\ne 0$

Therefore,

$x + 3 \ne 0$

$x \ne - 3$

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

Also,

$y \left(x + 3\right) = 7$

$y x + 3 y = 7$

$y x = 4 - 3 y$

$x = \frac{4 - 3 y}{y}$

The denominator is $\ne 0$

Therefore

$y \ne 0$

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

graph{(y-((7)/(x+3)))(y-0)=0 [-36.53, 36.52, -18.28, 18.27]}