Algebra II

Give the equations of any horizontal asymptotes for the graphs of the rational functions.

h(x)=(7x²-8x-5)/(8x²-3x+9)

g(x)=(x²+4x-8)/(x-8)

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1. divide top and bottom by x^2 to get

h(x) = (7 - 8/x - 5/x^2)/(8 - 3/x + 9/x^2)
as x approaches infinity, h(x) --> 7/8
so the horizontal axis is y = 7/8

the second one does not have a horizontal axis, but ...
g(x) = x + 12 + 88/(x-8)

there is an oblique asymptote at y = x + 12

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posted by Reiny

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