Question

find all horizontal asymptotes of the following function.
$f(x) = \frac{3x^2 - 27}{3x - 9}$
answer attempt 1 out of 2
one horizontal asymptote

Explanation:

Step1: Simplify the function

Factor numerator and denominator: $f(x)=\frac{3(x^2 - 9)}{3(x - 3)}=\frac{(x - 3)(x + 3)}{x - 3}=x + 3$ (for $x
eq3$)

Step2: Analyze horizontal asymptote

A linear function $y=x + 3$ has no horizontal asymptote (since $\lim_{x\to\pm\infty}(x + 3)=\pm\infty$, no finite limit)

Answer:

No horizontal asymptote