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Math Help - Confusion in sketching this graph

  1. #1
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    Confusion in sketching this graph

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

    There appears to be an x-intercept at 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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  2. #2
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    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.
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  3. #3
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    There is a horizontal asymptote at y= 1. There are no vertical asmptytotes because the denominator is never 0.
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  4. #4
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    Isn't horizontal asymptote at y = 0?
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  5. #5
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    Yes, of course. That was a typo. (That's my story and I'm sticking to it!)
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