# For what values of x, if any, does f(x) = 1/((x-1)(x-6))  have vertical asymptotes?

Dec 31, 2015

$x = 1 , 6$

#### Explanation:

Vertical asymptotes occur where the domain is undefined. That is, the spots when an error arises whenever $x$ is plugged in. For a rational function such as this one, such an error will occur whenever the denominator of a fraction is equal to $0$.

To find the spots where $f \left(x\right)$ has vertical asymptotes, set the denominator $\left(x - 1\right) \left(x - 6\right) = 0$.

$\left(x - 1\right) \left(x - 6\right) = 0$

$x - 1 = 0$
or
$x - 6 = 0$

$x = 1$
or
$x = 6$

Check a graph. The vertical asymptotes should occur when $x = 1 , 6$.

graph{1/((x-1)(x-6) [-7.51, 17.8, -6.34, 6.32]}