Question

What are the asymptote(s) and hole(s) of: `f(x)=(x^2+x-12)/(x^2-4)`?

Answer 1

Vertical Asymptotes at `x=2 and x=-2`
Horizontal Asymptote at `y=1`;

Explanation:

Vertical asymptote is found by solving the denominator equal to zero. i.e `x^2-4=0 or x^2=4 or x= +- 2`
Horizontal asymptote: Here the degree of numerator and denominator are same. Hence horizontal asymptote `y= 1/1=1` (numerator's leading co efficient/denominator's leading co efficient)
`f(x)= ((x-3)(x+4))/((x+2)(x-2))`Since there is no cancellation , there is no hole.[Ans}