SOLUTION: Find the horizontal asymptote, if any of the rational function. f(x)=8x^4+7x-8/x^2-8

Algebra ->  Rational-functions -> SOLUTION: Find the horizontal asymptote, if any of the rational function. f(x)=8x^4+7x-8/x^2-8      Log On


   

Question 137522: Find the horizontal asymptote, if any of the rational function.
f(x)=8x^4+7x-8/x^2-8
Found 2 solutions by edjones, Earlsdon:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
8x^4+7x-8/x^2-8
Since the degree of the numerator (x^4) is greater than the denominator (x^2) there is no horizontal asymptote.
.
Ed

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
At the point where a rational function, such as you have here, is undefined (denominator = 0), the graph is discontinuous (a break in the graph). At this (these) point(s), there may be an assymptote.
In your function:
f%28x%29+=+%288x%5E4%2B7x-8%29%2F%28x%5E2-8%29, the denominator will become zero when:
x%5E2-8+=+0 Solve the for x.
%28x%2Bsqrt%288%29%29%28x-sqrt%288%29%29+=+0
%28x%2B2sqrt%282%29%29%28x-2sqrt%282%29%29+=+0
x+=+-2sqrt%282%29 and x+=+2sqrt%282%29
So the graph of the function is discontinuous at these values of x. But this results in two VERTICAL assymptotes rather than horizontal assymptotes.
So the answer is, there are no horizontal assymptotes.
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%288x%5E2%2B7x-8%29%2F%28x%5E2-8%29%29