Practice Rational Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A rational function is a ratio of two polynomials: f(x) = P(x)/Q(x) where P and Q are polynomials and Q(x) \neq 0.
Rational functions are the "fractions" of the function world — they behave like polynomials except near the zeros of the denominator, where they blow up or have holes.
Example 1
mediumFind the vertical and horizontal asymptotes of f(x) = \frac{3x + 2}{x - 4}.
Example 2
hardFind all asymptotes and holes of f(x) = \frac{x^2 - 9}{x^2 - x - 6}.
Example 3
mediumFind the x-intercepts and vertical asymptotes of g(x) = \frac{x^2 - 1}{x^2 + 3x + 2}.
Example 4
hardFind all asymptotes (vertical, horizontal, and oblique) of f(x) = \frac{x^2 + 2x - 3}{x - 1}. Does the function have a hole or a vertical asymptote at x = 1?