Rational Functions in AP Precalculus

Vocabulary flashcards covering key concepts of rational functions from the lecture notes.

Rational Function

A function that is the ratio of two polynomial functions.

End Behavior

The behavior of a function as the input approaches positive or negative infinity.

Asymptote

A line that a graph approaches but never touches, often indicating the behavior of the function.

Domain of a Rational Function

All real values except those that make the denominator zero.

Vertical Asymptote

Occurs at x = a if x = a is a real zero of the denominator and not a zero of the numerator.

Real Zeros

Values of x that make the numerator zero but do not make the denominator zero.

Hole in a Function

Occurs when a real zero in the numerator is equal to a real zero in the denominator, causing the function to be undefined at that point.

Polynomial Long Division

An algebraic process used to divide polynomials, similar to numerical long division.

Slant Asymptote

A diagonal line that a graph approaches as x tends toward infinity, resulting from a linear polynomial in the numerator after dividing.

Factored Form

A representation of a polynomial or rational function that shows its real zeros, x-intercepts, and asymptotes.