$\displaystyle \displaystyle f(x)=\frac{x-1}{x^2+3}$

There appears to be an x-intercept at $\displaystyle x=1$, but I thought there is an asymptote at the x-axis since the denominator has a greater degree than the numerator?

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- Feb 26th 2011, 08:34 AMyoungb11Confusion in sketching this graph
$\displaystyle \displaystyle f(x)=\frac{x-1}{x^2+3}$

There appears to be an x-intercept at $\displaystyle x=1$, but I thought there is an asymptote at the x-axis since the denominator has a greater degree than the numerator? - Feb 26th 2011, 08:40 AMemakarov
Whether the x-axis is an asymptote describes the behavior of the function as x approaches infinity, and whether there is an x-intercept at x = 1 describes the behavior around x = 1. Both can be true.

- Feb 26th 2011, 02:39 PMHallsofIvy
There is a

**horizontal**asymptote at**y**= 1. There are no**vertical**asmptytotes because the denominator is never 0. - Feb 26th 2011, 03:03 PMemakarov
Isn't horizontal asymptote at y = 0?

- Feb 27th 2011, 04:35 AMHallsofIvy
Yes, of course. That was a typo. (That's my story and I'm sticking to it!)