Question
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)
h(x)=(7x²-8x-5)/(8x²-3x+9)
g(x)=(x²+4x-8)/(x-8)
Answers
Reiny
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
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