Polynomial and Rational Functions Glossary

The highest power of x in a polynomial. Determines end behavior and max number of zeros.

How f(x) behaves as x approaches positive or negative infinity.

A removable discontinuity where both numerator and denominator are zero due to a common factor.

A horizontal line y=L that the function approaches as x goes to infinity.

The coefficient of the highest-degree term. Along with degree, determines end behavior.

The number of times a factor (x-c) appears. Affects whether the graph crosses or bounces at that zero.

A function of the form f(x)=a_n*x^n+...+a_0 where n is a non-negative integer.

A function that is a ratio of two polynomials: f(x) = p(x)/q(x).

An oblique asymptote that occurs when numerator degree exceeds denominator degree by 1.

A shortcut for dividing a polynomial by a linear factor (x-c).

A vertical line x=a where the function approaches infinity. Denominator is zero, numerator is not.

A value c where f(c)=0. Corresponds to an x-intercept on the graph.