5. Rational Functions

Find a rational function ƒ having a graph with the given features.x-intercepts: (1, 0) and (3, 0)y-intercept: none vertical asymptotes: x=0 and x=2horizontal asymptote: y=1

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).

Provide a short answer to each question. Is ƒ(x)=1/x an even or an odd function? What symmetry does its graph exhibit?

Graph each rational function. ƒ(x)=4/(x-1)

Graph each rational function. ƒ(x)=(4x-2)/(3x+1)

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/x^2 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/x^2 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/(x^2+x−2)

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=2x^2/(x^2+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)=(x^2−1)/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)=(x^2+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)=(x^3+1)/(x^2+2x)

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x^2+x−12)/(x^2−4)