5. Rational Functions

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

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 the horizontal asymptote of each function.

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

Find the horizontal asymptote of each function.

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

Find all vertical asymptotes and holes of each function.

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

Find all vertical asymptotes and holes of each function.

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

Based only on the vertical asymptotes, which of the following graphs could be the graph of the given function? $f\(\left\)(x\(\right\))=\(\frac{x^2-4x}{x^2-x-12}\)$