5. Rational Functions

Solve each problem. Work each of the following. Sketch the graph of a function that does not intersect its horizontal asymptote y=1, has the line x=3 as a vertical asymptote, and has x-intercepts (2, 0) and (4, 0).

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

As x -> ∞, f(x) -> __

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. g(x)=1/(x−1)

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x² to graph each rational function. h(x)=1/(x−3)²+1

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

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

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

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²−1)/x

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²+1)/x

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x³+1)/(x²+2x)

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x²+x−12)/(x²−4)