Question

Find the horizontal asymptote of f of x equals quantity negative 2 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.

y = −1
y = −3
y = 1
y = 3

Answer 1

The horizontal asymptote of the function f(x) = (-2x^2 + 3x + 6) / (x^2 + 1) is y = -2.

Step-by-step explanation:

To find the horizontal asymptote of the function f(x) = (-2x^2 + 3x + 6) / (x^2 + 1), we need to evaluate the limit as x approaches infinity and negative infinity.

When x approaches infinity, the highest power term in the numerator and denominator dominates, which in this case is x^2. So, the limit is -2x^2 / x^2 = -2. Therefore, the horizontal asymptote is y = -2.