College Algebra

  1. Functions and Their Graphs
    1. The Cartesian Coordinate System
      1. Axes and Quadrants
        1. Plotting Points
          1. Ordered Pairs
            1. The Distance Formula
              1. The Midpoint Formula
                1. Graphing Equations by Plotting Points
                  1. Using Technology for Graphing
                  2. Introduction to Functions
                    1. Relations
                      1. Definition of a Relation
                        1. Domain and Range of a Relation
                          1. Representing Relations
                          2. Definition of a Function
                            1. Function as a Special Relation
                              1. Input-Output Relationship
                              2. Function Notation
                                1. f(x) Notation
                                  1. Evaluating Functions
                                    1. Function Values
                                    2. The Vertical Line Test
                                      1. Determining if a Graph Represents a Function
                                        1. Visual Identification
                                      2. Domain and Range of Functions
                                        1. Finding Domain from Equations
                                          1. Polynomial Functions
                                            1. Rational Functions
                                              1. Radical Functions
                                                1. Absolute Value Functions
                                                2. Finding Domain and Range from Graphs
                                                  1. Interval Notation
                                                    1. Set Notation
                                                      1. Restricted Domains
                                                      2. Properties of Graphs
                                                        1. Intercepts
                                                          1. Finding x-intercepts
                                                            1. Finding y-intercepts
                                                              1. Interpreting Intercepts
                                                              2. Symmetry
                                                                1. y-axis Symmetry
                                                                  1. x-axis Symmetry
                                                                    1. Origin Symmetry
                                                                      1. Tests for Symmetry
                                                                    2. Characteristics of Functions
                                                                      1. Increasing and Decreasing Intervals
                                                                        1. Relative Maxima and Minima
                                                                          1. Absolute Maxima and Minima
                                                                            1. Even and Odd Functions
                                                                              1. Algebraic Tests
                                                                                1. Graphical Identification
                                                                                2. Continuity
                                                                                  1. End Behavior
                                                                                  2. Library of Parent Functions
                                                                                    1. Constant Function
                                                                                      1. Identity Function
                                                                                        1. Absolute Value Function
                                                                                          1. Quadratic Function
                                                                                            1. Cubic Function
                                                                                              1. Square Root Function
                                                                                                1. Cube Root Function
                                                                                                  1. Reciprocal Function
                                                                                                    1. Greatest Integer Function
                                                                                                    2. Piecewise-Defined Functions
                                                                                                      1. Definition and Notation
                                                                                                        1. Evaluating Piecewise Functions
                                                                                                          1. Graphing Piecewise Functions
                                                                                                            1. Continuity of Piecewise Functions
                                                                                                            2. Transformations of Functions
                                                                                                              1. Vertical Shifts
                                                                                                                1. Horizontal Shifts
                                                                                                                  1. Reflections
                                                                                                                    1. Across the x-axis
                                                                                                                      1. Across the y-axis
                                                                                                                      2. Vertical Stretching and Shrinking
                                                                                                                        1. Horizontal Stretching and Shrinking
                                                                                                                          1. Combining Transformations
                                                                                                                            1. Order of Operations for Transformations
                                                                                                                            2. Operations on Functions
                                                                                                                              1. The Algebra of Functions
                                                                                                                                1. Sum of Functions
                                                                                                                                  1. Difference of Functions
                                                                                                                                    1. Product of Functions
                                                                                                                                      1. Quotient of Functions
                                                                                                                                      2. Domain of Combined Functions
                                                                                                                                        1. Evaluating Combined Functions
                                                                                                                                        2. Composition of Functions
                                                                                                                                          1. Definition and Notation
                                                                                                                                            1. Evaluating Composite Functions
                                                                                                                                              1. Domain of Composite Functions
                                                                                                                                                1. Decomposing Functions
                                                                                                                                                2. Inverse Functions
                                                                                                                                                  1. Definition of Inverse Functions
                                                                                                                                                    1. The Horizontal Line Test
                                                                                                                                                      1. Finding Inverse Functions Algebraically
                                                                                                                                                        1. Verifying Inverse Functions
                                                                                                                                                          1. Graphs of Functions and Their Inverses
                                                                                                                                                            1. Restricting Domains
                                                                                                                                                              1. Applications of Inverse Functions

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                                                                                                                                                            2. Equations and Inequalities

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                                                                                                                                                            4. Polynomial and Rational Functions