Question

Find the horizontal asymptote of the graph of the rational function. y = x^2 + 6 ———— 4^2 - 7 Identify the horizontal asymptote for the graph of the function.

Answer 1

Given:

$y\text{ = }\frac{x^2\text{ + 6}}{4x^2\text{ -7}}$

The rule for horizontal asymptote is shown below:

For the given rational function, the degree of the numerator is equal to the degree of the denominator.

Hence, the horizontal asymptote is:

$\begin{gathered} y\text{ = }\frac{1}{4} \\ \\ 1\text{ is the leading coefficient of the numerator} \\ and\text{ 4 is the leading coefficient of the denominator} \end{gathered}$

Answer:

$y\text{ = }\frac{1}{4}\text{ \lparen Option A\rparen}$