5. Rational Functions

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. f(x) = 2x/(x^2 - 9)

Use the graphs of the rational functions in choices A–D to answer each question.

There may be more than one correct choice. If ƒ represents the function, only one choice has a single solution to the equation ƒ(x)=3. Which one is it?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=(x²+3x+4)/(x-5)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=3/(x-5)

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

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(2x+6)/(x-4)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(4x²+25)/(x²+9)

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

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). $\text{ƒ}\left(x\right)=1/(x-2)$

Graph each rational function. ƒ(x)=(6-3x)/(4-x)

Graph each rational function. ƒ(x)=5x/(x²-1)

Graph each rational function. See Examples 5–9.

$\text{ƒ}\left(x\right)=\left[\right(x+6\left)\right(x-2\left)\right]/\left[\right(x+3\left)\right(x-4\left)\right]$

Graph each rational function. ƒ(x)=[(x+3)(x-5)]/[(x+1)(x-4)]

Graph each rational function. ƒ(x)=(x²+8x+16)/(x²+4x-5)

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