Question

Find the horizontal asymptote of

f(x) = -2x^2 + 3x + 6 over x^2 + 1.

A) y = -2
B) y = -1
C) y = 1
D) y = 2

Answer 1

The horizontal asymptote of the function is y = -2.

Step-by-step explanation:

The horizontal asymptote of a rational function can be found by comparing the degrees of the numerator and denominator polynomials.

In this case, both the numerator and denominator have the same degree, which is 2.

So, we need to compare the leading coefficients of the polynomials.

The leading coefficient of the numerator is -2, and the leading coefficient of the denominator is 1. Therefore, the horizontal asymptote of the function is y = -2.