# How do you graph y=(x^2-7x-60)/(x+3) using asymptotes, intercepts, end behavior?

Nov 7, 2016

See the graph below

#### Explanation:

As you cannot divide by $0$, $x = - 3$ is a vertical asymptotes.
As the degree of the numerator $>$ the degree of the denominator, we expect a slant asymptote. So we do a long division.
$\textcolor{w h i t e}{a a a}$${x}^{2} - 7 x - 60$$\textcolor{w h i t e}{a a a a}$∣$x + 3$
$\textcolor{w h i t e}{a a a}$${x}^{2} + 3 x$$\textcolor{w h i t e}{a a a a a a a a}$∣$x - 10$
$\textcolor{w h i t e}{a a a}$$0 - 10 x - 60$
$\textcolor{w h i t e}{a a a a a}$$- 10 x - 30$
$\textcolor{w h i t e}{a a a a a a a a a}$$0 - 30$

$y = \frac{{x}^{2} - 7 x - 60}{x + 3} = x - 10 - \frac{30}{x + 3}$
So $y = x - 10$ is an oblique asymptote
${\lim}_{\pm \infty} y = {\lim}_{\pm \infty} {x}^{2} / x = \pm \infty$
When $x = 0$$\implies$$y = - 20$
graph{(y-(x^2-7x-60)/(x+3))(y-x+10)=0 [-83.3, 83.26, -41.65, 41.7]}