# How do you find vertical, horizontal and oblique asymptotes for -7 / (x+4)?

Mar 21, 2018

$x = - 4$
$y = 0$

#### Explanation:

Consider this as the parent function:

$f \left(x\right) = \frac{\textcolor{red}{a} \textcolor{b l u e}{{x}^{n}} + c}{\textcolor{red}{b} \textcolor{b l u e}{{x}^{m}} + c}$ C's constants (normal numbers)

Now we have our function:

$f \left(x\right) = - \frac{7}{\textcolor{red}{1} \textcolor{b l u e}{{x}^{1}} + 4}$

It's important to remember the rules for finding the three types of asymptotes in a rational function:

Vertical Asymptotes: $\textcolor{b l u e}{\text{Set denominator = 0}}$

Horizontal Asymptotes: $\textcolor{b l u e}{\text{Only if "n = m, "which is the degree." " If " n=m, "then the H.A. is } \textcolor{red}{y = \frac{a}{b}}}$

Oblique Asymptotes: $\textcolor{b l u e}{\text{Only if " n > m " by " 1, "then use long division}}$

Now that we know the three rules, let's apply them:

V.A. $:$

$\left(x + 4\right) = 0$
$x = - 4$ $\textcolor{b l u e}{\text{ Subtract 4 from both sides}}$
$\textcolor{red}{x = - 4}$

H.A. $:$

$n \ne m$ therefore, the horizontal asymptote stays as $\textcolor{red}{y = 0}$

O.A. $:$

Since $n$ is not greater than $m$ (the degree of the numerator is not greater than the degree of the denominator by exactly 1) so there is no oblique asymptote.