# How do you write a rational function if the asymptotes of the graph are at #x=3# and #y=1#?

##### 1 Answer

Feb 11, 2018

#### Explanation:

Rational functions have vertical asymptotes where the denominator is zero and the numerator is non-zero (or has a zero of lower multiplicity). In our example we want a factor

Rational functions have non-zero horizontal asymptotes if the numerator and denominator are of equal degree. The

So the simplest rational function with the desired behaviour would be:

#f(x) = x/(x-3)#

graph{x/(x-3) [-8.5, 11.5, -4.64, 5.36]}