### Home > PC3 > Chapter 6 > Lesson 6.2.4 > Problem6-140

6-140.

Graph $r(x)=\frac{2x^2-4x-16}{x^2-9}$. State the locations of any holes and/or asymptotes.

$r(x)=\frac{2\left(x^2-2x-8\right)}{\left(x+3\right)\left(x-3\right)}$

$r(x)=\frac{2\left(x-4\right)\left(x+2\right)}{\left(x+3\right)\left(x-3\right)}$

Since none of the factors create a Giant $1$, there are no holes.
The vertical asymptotes are the values of $x$ that make the denominator $0$.
The horizontal asymptote is $y = 2$. (Why?)
The $x$-intercepts are the values of $x$ that make the numerator $0$.
The $y$-intercept occurs when $x = 0$.

Use this information to sketch a predicted graph of function. Then use a graphing calculator to check your work.
Be sure to identify and correct any mistakes.