5. Rational Functions

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

As $x\to -\infty ,f\left(x\right){\to }_{{}_{}}$_____

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

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

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.

$\text{ƒ}\left(x\right)=\frac{(x+7)}{(x+1)}$

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)

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)=1/(x+4)

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)/(x²+4x−21)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²-1)/(x+3)

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

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

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²-2x-3)/(2x²-x-10)

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

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

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

Work each problem. Which function has a graph that does not have a horizontal asymptote?

A. ƒ(x)=(2x-7)/(x+3)

B. ƒ(x)=3x/(x²-9)

C. ƒ(x)=(x²-9)/(x+3)

D. ƒ(x)=(x+5)/(x+2)(x-3)

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.