Question

what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?
$\bigcirc$ $y = 0$
$\bigcirc$ $y = 1$
$\bigcirc$ $y = 2$
$\bigcirc$ $y = 3$

Explanation:

Step1: Identify degrees of numerator/denominator

The numerator $x-2$ has degree 1, denominator $(x-3)^2 = x^2-6x+9$ has degree 2.

Step2: Apply horizontal asymptote rule

When degree of numerator < degree of denominator, the horizontal asymptote is $y=0$.

Answer:

y = 0