Section 1.4: Polynomial and Rational Functions

Polynomial Functions

A polynomial function is a function that can be written in the form:

f(x) = a_nxⁿ + a_{n - 1}x^{n - 1} + ... + a₁x + a₀

• n is a nonnegative integer, called the degree of the polynomial.
• The coefficients a₀, a₁, ..., a_n are real numbers with a_n ≠ 0.
• The domain of a polynomial function is the set of all real numbers.

Rational Functions

A rational function is any function that can be written in the form:

f(x) = n(x)/d(x), d(x) ≠ 0

• n(x) and d(x) are polynomials.
• The domain of a rational function is the set of all real numbers such that d(x) ≠ 0.