SOLUTION: Write a rational function with no vertical asymptote and no holes.

Algebra ->  Test -> SOLUTION: Write a rational function with no vertical asymptote and no holes.       Log On


   

Question 706221: Write a rational function with no vertical asymptote and no holes.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%5E3%2B2x%5E2-8x%29%2F%28x%5E2%2B1%29 The denominator x%5E2%2B1 is never zero, so there are no vertical asymptotes and no holes.
(You need zeros in the denominator for those).
The graph is shown in red below.


EXTRA:
It has a slanted asymptote (shown in green) because

and abs%28%289x%2B2%29%2F%28x%5E2%2B1%29%29 gets smaller and smaller as x%5E2 grows larger and larger.