# How do you graph #f(x)=x/(x^2-9)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

Below

#### Explanation:

Therefore, the vertical asymptotes are

For our horizontal asymptote, we look at the degree of our numerator and denominator. Since the degree of the numerator is less than the denominator, then

Another way you can think of it is it you sub random numbers into the

For our intercepts,

When

When

Therefore,

Drawing up our asymptotes (horizontal and vertical) and our intercept, we should be able to draw our graph. Remember that for our asymptotes, it only affects the ends of the graph as it is approaching the asymptotes from above or below. Our graph can actually cross the asymptotes.

graph{x/(x^2-9) [-10, 10, -5, 5]}