# For what values of x, if any, does #f(x) = 1/((x-2)(x-1)(x-3)) # have vertical asymptotes?

##### 1 Answer

Apr 26, 2016

Vertical asymptotes exist at

#### Explanation:

A vertical asymptote is caused in a rational function when there is a zero in the denominator while the numerator is non-zero. For our function that corresponds to :

which means that any of the factors on the right hand side could be zero. By inspection we see that this happens when

Therefore, these are the values where the vertical asymptotes exist. Graphing the function confirms our results.

graph{1/((x-3)(x-2)(x-1)) [-1, 5, -55, 55]}