3. Polynomial and Rational Functions

Sketch the graph of the function $f\left(x\right)=\frac{1}{x^2}$. Identify the asymptotes on the graph.

Based only on the vertical asymptotes, which of the following graphs could be the graph of the given function?

$f\left(x\right)=\frac{x^2-4x}{x^2-x-12}$

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{-5x}{{(2x-3)}^2}$

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{x^2-2x}{2x^3-x^2-6x}$