Precalculus

  1. Exponential and Logarithmic Functions
    1. Exponential Functions
      1. Definition and Properties
        1. Base and Exponent
          1. Domain and Range
          2. Laws of Exponents
            1. Product Rule
              1. Quotient Rule
                1. Power Rule
                  1. Negative Exponents
                    1. Zero Exponent
                    2. Graphs of Exponential Functions
                      1. Exponential Growth
                        1. Exponential Decay
                          1. Horizontal Asymptotes
                            1. y-intercept
                            2. The Natural Base e
                              1. Definition of e
                                1. Natural Exponential Function
                                  1. Properties of e
                                  2. Exponential Models
                                    1. Compound Interest
                                      1. Simple Interest
                                        1. Compound Interest Formula
                                          1. Continuous Compounding
                                          2. Population Growth
                                            1. Radioactive Decay
                                              1. Newton's Law of Cooling
                                            2. Logarithmic Functions
                                              1. Definition of Logarithms
                                                1. Inverse of Exponential Functions
                                                  1. Logarithmic Form vs Exponential Form
                                                  2. Common Logarithms
                                                    1. Base 10 Logarithms
                                                      1. Calculator Use
                                                      2. Natural Logarithms
                                                        1. Base e Logarithms
                                                          1. ln Notation
                                                          2. Graphs of Logarithmic Functions
                                                            1. Domain and Range
                                                              1. Vertical Asymptotes
                                                                1. x-intercept
                                                                  1. Inverse Relationship with Exponentials
                                                                  2. Converting Between Forms
                                                                    1. Exponential to Logarithmic
                                                                      1. Logarithmic to Exponential
                                                                    2. Properties of Logarithms
                                                                      1. Product Rule
                                                                        1. Quotient Rule
                                                                          1. Power Rule
                                                                            1. Change-of-Base Formula
                                                                              1. Expanding Logarithmic Expressions
                                                                                1. Condensing Logarithmic Expressions
                                                                                  1. Common Logarithm Properties
                                                                                    1. Natural Logarithm Properties
                                                                                    2. Exponential and Logarithmic Equations
                                                                                      1. Solving Exponential Equations
                                                                                        1. Same Base Method
                                                                                          1. Taking Logarithms of Both Sides
                                                                                            1. Using Properties of Logarithms
                                                                                            2. Solving Logarithmic Equations
                                                                                              1. Converting to Exponential Form
                                                                                                1. Using Properties of Logarithms
                                                                                                  1. Checking for Extraneous Solutions
                                                                                                  2. Applications and Modeling
                                                                                                    1. Compound Interest Problems
                                                                                                      1. Growth and Decay Problems
                                                                                                        1. pH Scale
                                                                                                          1. Richter Scale
                                                                                                            1. Carbon Dating
                                                                                                              1. Sound Intensity

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                                                                                                          3. Polynomial and Rational Functions

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                                                                                                          5. Trigonometric Functions