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!
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
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