# How do you find the domain of f(x) = 8 /( x + 4)?

Jul 13, 2017

Domain: $\left(- \infty , - 4\right) \cup \left(- 4 , \infty\right)$

#### Explanation:

The domain of a rational function is all the values except for those which that make it undefined. In other words, the denominator of a rational function cannot be $0$.

To find which values exactly make the rational function undefined, we set the denominator not equal to $0$ and solve for $x$

$x + 4 \ne 0$

$x + \cancel{4 - 4} \ne 0 - 4$

$x \ne - 4$

What we have solved for tells us the values ($x -$values to be precise) that cannot be in the domain.

Therefore our domain is all real numbers except $- 4$. In interval notation, this is:

$\left(- \infty , - 4\right) \cup \left(- 4 , \infty\right)$

What this tells us about the graph as well is that there is a vertical asymptote defined by the line $x = - 4$ (See graph)

graph{8/(x+4) [-23.37, 16.63, -9.44, 10.56]}

Jul 13, 2017

Domain of $f \left(x\right) = \left(- \infty , - 4\right) \cup \left(- 4 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \frac{8}{x + 4}$

$f \left(x\right)$ is defined for all x except $x = - 4$ where the function is undefined.

$\therefore$ the domain of $f \left(x\right) = \forall x \in \mathbb{R} : x \ne - 4$

In interval notation: Domain of $f \left(x\right) = \left(- \infty , - 4\right) \cup \left(- 4 , + \infty\right)$

The domain can be seen on the graph of $f \left(x\right)$ below.

graph{8/(x+4) [-32.47, 32.48, -16.24, 16.23]}