What are the asymptotes of the function fx x2 x 62x2 2So

What are the asymptotes of the function f(x) = x^2 + x - 6/2x^2 - 2?

Solution

lets first calculate the vertical asymptotes as

so we shall set denominator equal to zero and solve

2x2-2 = 0

x2= 2/2

x2=1

x = +-1 , the 2 vertical asymptotes are +-1

now to find the horizontal aymptotes , we see the degree of numerator or denominator are equal , so we take the ratio of the highest degree terms of numnerator and denominator

x2/2x2 = 1/2 , which would be our horizontal asymptote