Advanced Algebra II Exam Preparation Flashcards

These flashcards cover key concepts from Advanced Algebra II, focusing on polynomial functions, graphing, and theorems relevant to the subject.

Odd Functions

A function that satisfies f(-x) = -f(x) for all x in the domain.

Even Functions

A function that satisfies f(-x) = f(x) for all x in the domain.

Turning Points

Points at which a graph changes from increasing to decreasing or vice versa.

Boundedness Theorem

A theorem stating certain conditions under which a polynomial has no real roots greater or less than specific bounds.

Rational Functions

Functions defined by the ratio of two polynomials.

Vertical Asymptotes

Lines x = a where a rational function approaches infinity as x approaches a.

Horizontal Asymptotes

Horizontal lines that the graph of a function approaches as x approaches infinity or negative infinity.

Oblique (Slant) Asymptotes

A slant line that the graph of a function approaches when the degree of the numerator is one more than the degree of the denominator.

Multiplicity of a Zero

The number of times a particular zero occurs for a polynomial function.

Intermediate Value Theorem

A theorem stating that if f is continuous on [a, b] and f(a) and f(b) have different signs, there is at least one c in (a, b) such that f(c) = 0.

End Behavior

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

Synthetic Division

A simplified method of dividing a polynomial by a linear divisor.

Rational Root Theorem

A theorem that provides a method for finding all possible rational roots of a polynomial equation.

Graphing Polynomials

The process of drawing the curve of a polynomial function based on its zeros, multiplicity, and end behavior.

Asymptotes

Lines that a graph approaches but never touches or crosses.

Factoring

The process of breaking down a polynomial into simpler or irreducible components.