Given the function Find vertical asymptote horizontal asympt

Given the function

Find vertical asymptote

horizontal asymptote

slant asymptote

(If the function does not have an asymptote state: none)

Solution

VerticaL Asmyptote :

For a rational function, the vertical asymptote is at point where function is not defined.

The only values that could be disallowed are those that give me a zero in the denominator.

So x^2+3x = 0 => x(x+3)= 0 => x = 0 and x = -3

so vertical asmptotes are x = 0 and x = -3

Horizontal Asymptote :

if the denominator\'s degree is greater (by any margin), then you have a horizontal asymptote at y = 0

So here Horizontal Asmyptote is y = 0.

Slant Asmptote:

Since degree of the numerator is not one more degree of denominator, then there are no slant asymptotes.