College Algebra

  1. Polynomial and Rational Functions
    1. Quadratic Functions
      1. Standard Form
        1. Vertex Form
          1. Converting Between Forms
            1. Graphing Parabolas
              1. Vertex
                1. Axis of Symmetry
                  1. Direction of Opening
                    1. x-intercepts and y-intercept
                    2. Maximum and Minimum Values
                      1. Applications and Modeling
                        1. Optimization Problems
                          1. Projectile Motion
                            1. Business Applications
                          2. Polynomial Functions of Higher Degree
                            1. General Form
                              1. Degree and Leading Coefficient
                                1. End Behavior
                                  1. Leading Coefficient Test
                                    1. Behavior at Infinity
                                    2. Zeros of Polynomial Functions
                                      1. Real Zeros
                                        1. Complex Zeros
                                          1. Rational Zeros
                                          2. Multiplicity of Zeros
                                            1. Effect on Graph Behavior
                                              1. Touching vs. Crossing x-axis
                                              2. Graphing Polynomial Functions
                                                1. Finding Zeros
                                                  1. Analyzing End Behavior
                                                    1. Sketching Graphs
                                                    2. The Intermediate Value Theorem
                                                    3. Dividing Polynomials
                                                      1. Long Division of Polynomials
                                                        1. Setup and Algorithm
                                                          1. Dividend, Divisor, Quotient, Remainder
                                                          2. Synthetic Division
                                                            1. When Applicable
                                                              1. Step-by-Step Process
                                                                1. Advantages and Limitations
                                                                2. Applications of Division
                                                                3. Theorems about Zeros of Polynomials
                                                                  1. The Remainder Theorem
                                                                    1. The Factor Theorem
                                                                      1. The Rational Zero Theorem
                                                                        1. Listing Possible Rational Zeros
                                                                          1. Testing Candidates
                                                                          2. Descartes' Rule of Signs
                                                                            1. The Fundamental Theorem of Algebra
                                                                              1. The Linear Factorization Theorem
                                                                                1. Finding All Zeros
                                                                                  1. Real and Complex Zeros
                                                                                    1. Using Technology
                                                                                  2. Rational Functions
                                                                                    1. Definition and General Form
                                                                                      1. Domain of Rational Functions
                                                                                        1. Vertical Asymptotes
                                                                                          1. Finding Vertical Asymptotes
                                                                                            1. Behavior Near Asymptotes
                                                                                            2. Horizontal Asymptotes
                                                                                              1. Rules for Finding
                                                                                                1. End Behavior Analysis
                                                                                                2. Slant Asymptotes
                                                                                                  1. When They Occur
                                                                                                    1. Finding Slant Asymptotes
                                                                                                    2. Holes in Graphs
                                                                                                      1. Removable Discontinuities
                                                                                                        1. Finding Holes
                                                                                                        2. Graphing Rational Functions
                                                                                                          1. Complete Analysis Process
                                                                                                            1. Intercepts
                                                                                                              1. Asymptotes
                                                                                                                1. Sign Analysis
                                                                                                                2. Applications of Rational Functions

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                                                                                                              3. Functions and Their Graphs

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                                                                                                              5. Exponential and Logarithmic Functions