5. Rational Functions

Use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. g(x)=1/(x+1) − 2

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=(x²−9)/(x−3)

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As $x\to 1^{+},f\left(x\right)\to$ __

Find the horizontal asymptote of each function.

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

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4.

$\text{ƒ}\left(x\right)=(x^2+4)/(x-1)$

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 domain of each rational function. f(x)=5x/(x−4)

Follow the seven steps to graph each rational function. f(x)=x⁴/(x²+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\(\right\))=\(\frac{x^2+10x+25}{2x^2+8x-10}\)$

Graph each rational function. ƒ(x)=(2x+1)/(x²+6x+8)

Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.

Find all vertical asymptotes and holes of each function.

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

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. g(x)=(x−3)/(x²−9)