3. Polynomial and Rational Functions

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{x^2+10x+25}{2x^2+8x-10}$

Find the horizontal asymptote of each function.

$f\left(x\right)=\frac{x^2+4x}{2x^3+8x^2}$

Find all vertical asymptotes and holes of each function.

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

Find all vertical asymptotes and holes of each function.

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

Find the horizontal asymptote of each function.

$f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}$

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 the horizontal asymptote of each function.

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