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

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

Maddox Koch · Accepted Answer

You know this graph can&#039;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                     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.

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

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