Asymptotes of

Question

f(x)= x^2+2x-15 / x^3+1?

Answer 1

The rational function

to find the vertical asympotote.

To find vertical asymptotes are found  by solving denominator = 0

Aplly the formula

Apply zero product property.

First case solution x = - 1

Noe solve

In the second case roots are imaginary.

Therefore, vertical asymptote is x = -1

To find horizontal asymptote.

Degree of the numarator = 2 and the degree of denominator = 3.

If the degree of the numerator is less than the degree of the denominator, the line y = 0 (x - axis)

is the horizontal asymptote.

Vertical asympotote x = -1 and horizontal asympotote y = 0.