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

How do you graph $f\left(x\right)=\frac{{x}^{2}-1}{x}$ using holes, vertical and horizontal asymptotes, x and y intercepts?
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You know this graph can't exist at x=0, since that would make the denominator equal 0. Because the polynomial on the top is of a bigger degree, there is a slant asymptote. Dividing the initial terms, we get $\frac{{x}^{2}}{x}=x$, so there is a slant asymptote at y=x.
Since we can factor the top into (x−1)(x+1), we know the function has two solutions at $x=±1$.

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 pblackict 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.