Rational Functions

A rational function is one such that $f(x) = \frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$; the domain of a rational function can be calculated.

A rational function can have at most one horizontal or oblique asymptote, and many possible vertical asymptotes; these can be calculated.

The $x$-intercepts of rational functions are found by setting the polynomial in the numerator equal to $0$ and solving for $x$.

A rational expression can be treated like a fraction, and can be manipulated via multiplication and division.

Partial fraction decomposition is a procedure used to reduce the degree of either the numerator or the denominator of a rational function.