# How do you graph #f(x)=(x^2-1)/x# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

You have a vertical asymptote at x=0 because that would make the denominator equal zero. There's a slant asymptote at

#### Explanation:

You know this graph can't exist at

Since we can factor the top into

Plotting these solutions and following the asymptotes makes this a straightforward graph to sketch: graph{(x^2-1)/x [-10, 10, -5, 5]}

Also, not all rational functions are so easy to predict the behavior of, so creating a table of x and y values is always a good idea! And if you need more information about how to find the asymptotes, look here.