How to find the horizontal asymptote of this function
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How to find the horizontal asymptote of this function

[From: ] [author: ] [Date: 13-07-04] [Hit: ]
then OK.Or,limit((2*x^2 + x - 4)/( - x^2 - 5*x + 6),limit((2*x^2 + x - 4)/( - x^2 - 5*x + 6),......
Could anyone please tell me the steps to find the horizontal asymptote of this function:
y=(2x^2+x-4) / (-x^2-5x+6)

(Here's the equation put more clearly and it's graph: http://www.wolframalpha.com/input/?i=y%3D+%282x%5E2%2Bx-4%29+%2F+%28-x%5E2-5x%2B6%29)

It's a weird kind of rational function, and I was only taught how to find the asymptotes of normal rational functions...

Thank you for your help!

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Since the numerator and denominator are of the same degree, the HA is just the ratio of the leading coefficients, y = 2/(-1) = -2

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Download Graph 4.4 from www.padowan.dk for free.

On "Axes", change the range of X edge from - 100 to 100, then "OK".

On "Function I Insert function", type (2*x^2 + x - 4) / ( - x^2 - 5*x + 6), then "OK".

You'll see the Horizontal Asymptote at x = - 2

Or,

limit((2*x^2 + x - 4)/( - x^2 - 5*x + 6), x = ∞ ) = - 2

limit((2*x^2 + x - 4)/( - x^2 - 5*x + 6), x = - ∞ ) = - 2
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