Question

question
find all horizontal asymptotes of the following function.
$f(x)=\frac{3x^{2}-243}{6x + 16}$
no horizontal asymptotes
one horizontal asymptote
two horizontal asymptotes
one horizontal asymptote

Explanation:

Step1: Recall the rule for horizontal asymptotes

For a rational function \(f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}\), if \(n>m\), there is no horizontal asymptote. Here, the degree of the numerator \(n = 2\) (for \(3x^2-243\)) and the degree of the denominator \(m=1\) (for \(6x + 16\)).

Answer:

No Horizontal Asymptotes