# How do you identify the vertical asymptotes of f(x) = (10)/(x^2-7x-30)?

Oct 6, 2015

Well, as $x \to - 3$ then $f \left(x\right) \to \infty$
and as $x \to 10$ then $f \left(x\right) \to \infty$

#### Explanation:

To get to this answer, you'll first have to factorize the denominator, to see when this gets (closer and closer) to zero.
${x}^{2} - 7 x - 30 = \left(x + 3\right) \left(x - 10\right)$

Hence $x = - 3 , x = 10$ vertical asymptotes.

The graph for $f \left(x\right)$ is

graph{10/(x^2-7x-30) [-20.27, 20.26, -10.14, 10.13]}