5. Rational Functions

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

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

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)

Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x−2)/(x²−4)

Find the domain of each rational function. h(x)=(x+7)/(x²−49)

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x+2)/(x²+x−6)

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)

In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. x/(2x+6) − 9/(x²−9)

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

Based only on the vertical asymptotes, which of the following graphs could be the graph of the given function? $f\(\left\)(x\(\right\))=\(\frac{x^2-4x}{x^2-x-12}\)$

In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. 5x²/(x²−4) ⋅ (x²+4x+4)/(10x³)