Precalculus

3.

Polynomial and Rational Functions

3.1.

Quadratic Functions

3.1.1.

3.1.2.

3.1.3.

3.1.4.

Finding the Vertex

3.1.5.

Axis of Symmetry

3.1.6.

Graphing Quadratic Functions

3.1.6.1.

Opening Direction

3.1.6.2.

Vertex and Intercepts

3.1.6.3.

Domain and Range

3.1.7.

Applications and Modeling

3.1.7.1.

Projectile Motion

3.1.7.2.

Optimization Problems

3.1.7.3.

Revenue and Profit Models

3.2.

Polynomial Functions of Higher Degree

3.2.1.

General Form of Polynomial Functions

3.2.2.

Degree and Leading Coefficient

3.2.3.

Graphs of Polynomial Functions

3.2.3.1.

Smooth and Continuous

3.2.3.2.

3.2.3.3.

3.2.4.

3.2.4.1.

Leading Coefficient Test

3.2.4.2.

Behavior as x approaches infinity

3.2.5.

Zeros of Polynomial Functions

3.2.5.1.

3.2.5.2.

3.2.5.3.

3.2.6.

Multiplicity of Zeros

3.2.6.1.

3.2.6.2.

3.2.6.3.

Graphical Behavior at Zeros

3.2.7.

The Intermediate Value Theorem

3.2.7.1.

Statement and Applications

3.2.7.2.

3.3.

Polynomial Division

3.3.1.

Long Division of Polynomials

3.3.1.1.

Step-by-Step Process

3.3.1.2.

Dividend, Divisor, Quotient, Remainder

3.3.2.

Synthetic Division

3.3.2.1.

When to Use Synthetic Division

3.3.2.2.

Step-by-Step Process

3.3.2.3.

3.3.3.

The Division Algorithm

3.3.4.

The Remainder Theorem

3.3.5.

The Factor Theorem

3.4.

Zeros of Polynomial Functions

3.4.1.

The Rational Zero Theorem

3.4.1.1.

Possible Rational Zeros

3.4.1.2.

Testing Candidates

3.4.2.

The Fundamental Theorem of Algebra

3.4.3.

The Linear Factorization Theorem

3.4.4.

Descartes' Rule of Signs

3.4.4.1.

Positive Real Zeros

3.4.4.2.

Negative Real Zeros

3.4.5.

Upper and Lower Bounds

3.4.6.

Finding All Zeros

3.4.6.1.

Real and Complex Zeros

3.4.6.2.

Using Technology

3.5.

Rational Functions

3.5.1.

Definition and General Form

3.5.2.

Domain of Rational Functions

3.5.2.1.

Excluded Values

3.5.3.

Vertical Asymptotes

3.5.3.1.

Finding Vertical Asymptotes

3.5.3.2.

Behavior Near Asymptotes

3.5.4.

Horizontal Asymptotes

3.5.4.1.

Rules for Finding

3.5.4.2.

3.5.5.

Slant Asymptotes

3.5.5.1.

When They Occur

3.5.5.2.

Finding Slant Asymptotes

3.5.6.

Holes in Graphs

3.5.6.1.

Removable Discontinuities

3.5.6.2.

3.5.7.

Graphing Rational Functions

3.5.7.1.

Step-by-Step Process

3.5.7.2.

3.5.7.3.

3.5.7.4.

3.5.8.

Applications of Rational Functions

3.5.8.1.

3.5.8.2.

Concentration Problems

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2. Functions and Their Graphs

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4. Exponential and Logarithmic Functions