5. Rational Functions

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to -3^{-}$, $f\left(x\right)\to$____

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²+x−6)/(x−3)

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). $\text{ƒ}\left(x\right)=-1/(x-2)$

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. r(x)=x/(x²+4)

Graph the rational function using transformations.

$f\left(x\right)=-\frac{1}{x}+3$

Graph the rational function using transformations.

$f\left(x\right)=\frac{1}{\left(x+3\right)^2}-2$

Graph the rational function.

$f\left(x\right)=\frac{x+3}{x^2+5x+6}$