College Algebra

  1. Exponential and Logarithmic Functions
    1. Exponential Functions
      1. Definition and Properties
        1. Exponential Growth
          1. Exponential Decay
            1. Graphing Exponential Functions
              1. Domain and Range
                1. Horizontal Asymptotes
                  1. Intercepts
                    1. Transformations
                    2. The Natural Base e
                      1. Definition and Approximation
                        1. Natural Exponential Function
                        2. Applications of Exponential Functions
                          1. Population Growth
                            1. Radioactive Decay
                              1. Compound Interest
                                1. Cooling and Heating Models
                              2. Logarithmic Functions
                                1. Definition as Inverse of Exponential
                                  1. Logarithmic Form vs. Exponential Form
                                    1. Common Logarithms
                                      1. Natural Logarithms
                                        1. Graphing Logarithmic Functions
                                          1. Domain and Range
                                            1. Vertical Asymptotes
                                              1. Intercepts
                                                1. Transformations
                                                2. Evaluating Logarithms
                                                  1. Exact Values
                                                    1. Using Technology
                                                  2. Properties of Logarithms
                                                    1. Product Property
                                                      1. Quotient Property
                                                        1. Power Property
                                                          1. Change of Base Formula
                                                            1. Expanding Logarithmic Expressions
                                                              1. Condensing Logarithmic Expressions
                                                              2. Exponential and Logarithmic Equations
                                                                1. Solving Exponential Equations
                                                                  1. Same Base Method
                                                                    1. Taking Logarithms of Both Sides
                                                                      1. Using Properties
                                                                      2. Solving Logarithmic Equations
                                                                        1. Converting to Exponential Form
                                                                          1. Using Properties of Logarithms
                                                                            1. Checking for Extraneous Solutions
                                                                            2. Applications
                                                                              1. Growth and Decay Problems
                                                                                1. Compound Interest
                                                                                  1. Half-Life Problems
                                                                                2. Mathematical Modeling with Exponential and Logarithmic Functions
                                                                                  1. Exponential Growth Models
                                                                                    1. Exponential Decay Models
                                                                                      1. Logistic Growth Models
                                                                                        1. Logarithmic Models
                                                                                          1. Fitting Models to Data

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                                                                                        4. Polynomial and Rational Functions

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                                                                                        6. Systems of Equations and Inequalities