Question

What is the horizontal asymptote for (x^2 - 2)/(x^2 - 4)?

a) 0
b) 1
c) 2
d) There is no horizontal asymptote

Answer 1

The horizontal asymptote of the function (x^2 - 2)/(x^2 - 4) is 1, since the degrees of the numerator and denominator are the same, and the leading coefficients are both 1. Option number b is correct .

Step-by-step explanation:

The question asks about finding the horizontal asymptote of the function (x^2 - 2)/(x^2 - 4). To find the horizontal asymptote of a rational function, we compare the degrees of the numerator and denominator.

In this case, the degrees are the same (both have x^2 as the highest term), so the horizontal asymptote is the leading coefficient of the numerator divided by the leading coefficient of the denominator. Since both the numerator and denominator have the leading coefficient as 1 for x^2, the horizontal asymptote is 1, making the answer option b) 1.