SOLUTION: Use limits to describe the behavior of the rational function near the indicated asymptote. f(x) = (4x^2 - 3)/(x^2 + 1) Describe the behavior of the function near its horizontal

Algebra ->  Functions -> SOLUTION: Use limits to describe the behavior of the rational function near the indicated asymptote. f(x) = (4x^2 - 3)/(x^2 + 1) Describe the behavior of the function near its horizontal       Log On


   

Question 1131911: Use limits to describe the behavior of the rational function near the indicated asymptote.
f(x) = (4x^2 - 3)/(x^2 + 1)
Describe the behavior of the function near its horizontal asymptote (the end behavior)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3Einfinity%29+%284+x%5E2+-+3%29%2F%28x%5E2+%2B+1%29+=+4
A horizontal asymptote is
%284+x%5E2+-+3%29%2F%28x%5E2+%2B+1%29->4 as x-> ±infinity
A horizontal asymptote is in this case a horizontal line y=4 that indicates where a function flattens out as x gets very large or very small. A function may touch or pass through a horizontal asymptote.


Image and video hosting by TinyPic

as you can see on the graph, a function didn't touch or pass through a horizontal asymptote