Rational Function¶
Definition ¶
A rational function is a mathematical function expressed as the quotient of two polynomials. It takes the form:
\(f(x) = \frac{P(x)}{Q(x)}\)
where \(P(x)\) and \(Q(x)\) are polynomials, and \(Q(x)\) is not the zero polynomial.
The domain of a rational function is the set of all \(x\) values for which the denominator \(Q(x)\) is not equal to zero because division by zero is undefined. The range of the function is determined by the behavior of the numerator and denominator polynomials.
Here are a few examples of rational functions:
- \(f(x) = \frac{x^2 + 1}{x - 3}\)
- \(g(x) = \frac{2x - 5}{x^2 + x + 1}\)
- \(h(x) = \frac{1}{x}\)