5. Rational Functions

Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?

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

As x -> 1^-, f(x) -> __

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

As x -> -∞, f(x) -> __

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

As x -> 1^+, f(x) -> __

Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x+7)/(x+1)

In Exercises 21–36, 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)=(x^2−9)/(x−3)

Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=1/(x+4)

In Exercises 21–36, 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)/(x^2−9)

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. h(x)=(x+7)/(x^2+4x−21)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2-1)/(x+3)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2+4)/(x-1)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2-2x-3)/(2x^2-x-10)

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. h(x)=1/x + 2

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. g(x)=1/(x+1) − 2

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