Question

State the Horizontal Asymptote for the following function: f(x)=4–2x²/4x2 - 6x

Answer 1

Given data:

$f(x)=\frac{4-2x^2}{4x^2-6x}$

For these function we will use

$f(x)=\frac{p(x)}{q(x)};\text{ q(x)}\ne0$

Here, The degree of p = degree of q = 2

So, the horizontal asymptote is by taking the ratio of the leading terms.

The horizontal asymptote is given as,

$\begin{gathered} y=\frac{-2}{4} \\ =-\frac{1}{2} \end{gathered}$

Thus, the horizontal asymptote is -1/2.