Write a rational function with no veritas al asymptotes and no holes. explain

Question

asked Jun 25, 2023 35.0k views

1 Answer

Mathica · Answer 1 · 2023-06-30T21:58:00+0000

Question:

write a rational function with no vertical asymptotes and no holes. explain.

Solution:

Let the following rational function:

$f(x)\text{ = }(x^3+2x^2-8x)/(x^2+1)$

notice that the denominator is never zero:

$x^2+\text{ 1 > 0}$

so there are no vertical asymptotes and no holes. (You need zeros in the denominator for those). The graph is shown below.