Find asymptotes of the graph

Question

Given g(x) = x^2 + 2 / x^2 - 9, use limits to find the horizontal and vertical asymptotes. Then drawthe graph showing asympototes as dahsed lines.

Answer 1

To find the vertical asymptotes, look at the denominator. Will have to factor it first. x²-9 = (x-3)(x+3) Set these factors equal to zero and solve.

x+3=0 and x-3=0 Solving

x=-3 and x=3

Next is the horizontal asymptote. The degree of the numerator and denominator are both 2. In this case you use the coefficients, y=1.