5. Rational Functions

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

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

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)=x⁴/(x²+2)

Solve each problem. Find a rational function ƒ having the graph shown.

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)

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)

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. (1 − 3/(x+2)) / (1 + 1/(x−2))

In Exercises 1–8, find the domain of each rational function. f(x)=5x/(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)/(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). $\text{ƒ}\left(x\right)=-1/(x-2{)}^2$