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)

Provide a short answer to each question. What is the domain of the function $\text{ƒ}\left(x\right)=\frac{1}{x^2}$? What is its range?

Follow the seven steps to graph each rational function. f(x)=−x/(x+1)

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

As $x\to \infty ,f\left(x\right)\to$_____

Graph each rational function. ƒ(x)=(9x²-1)/(x²-4)

Follow the seven steps to graph each rational function. f(x)=4x/(x−2)

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)

Provide a short answer to each question. What is the equation of the vertical asymptote of the graph of y=[1/(x-3)]+2? Of the horizontal asymptote?

Graph the rational function using transformations.

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

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. r(x) = (x^2 + 4x + 3)/(x + 2)^2

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)=(x³+1)/(x²+2x)

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+1)/x