**1.1 Graphing Basics **

1.1.1 Using the Cartesian System

1.1.2 Thinking Visually

**1.2 Relationships between Two Points **

1.2.1 Finding the Distance between Two Points

1.2.2 Finding the Second Endpoint of a Segment

**1.3 Relationships among Three Points **

1.3.1 Collinearity and Distance

1.3.2 Triangles

**1.4 Circles **

1.4.1 Finding the Center-Radius Form of the Equation of a Circle

1.4.2 Decoding the Circle Formula

1.4.3 Finding the Center and Radius of a Circle

1.4.4 Solving Word Problems Involving Circles

**1.5 Graphing Equations **

1.5.1 Graphing Equations by Locating Points

1.5.2 Finding the x- and y-Intercepts of an Equation

**1.6 Function Basics **

1.6.1 Functions and the Vertical Line Test

1.6.2 Identifying Functions

1.6.3 Function Notation and Finding Function Values

**1.7 Working with Functions **

1.7.1 Determining Intervals Over Which a Function Is Increasing

1.7.2 Evaluating Piecewise-Defined Functions for Given Values

1.7.3 Solving Word Problems Involving Functions

**1.8 Function Domain and Range **

1.8.1 Finding the Domain and Range of a Function

1.8.2 Domain and Range: One Explicit Example

1.8.3 Satisfying the Domain of a Function

**1.9 Linear Functions: Slope **

1.9.1 An Introduction to Slope

1.9.2 Finding the Slope of a Line Given Two Points

1.9.3 Interpreting Slope from a Graph

1.9.4 Graphing a Line Using Point and Slope

**1.10 Equations of a Line **

1.10.1 Writing an Equation in Slope-Intercept Form

1.10.2 Writing an Equation Given Two Points

1.10.3 Writing an Equation in Point-Slope Form

1.10.4 Matching a Slope-Intercept Equation with Its Graph

1.10.5 Slope for Parallel and Perpendicular Lines

**1.11 Graphing Functions **

1.11.1 Graphing Some Important Functions

1.11.2 Graphing Piecewise-Defined Functions

1.11.3 Matching Equations with Their Graphs

**1.12 Manipulating Graphs: Shifts and Stretches **

1.12.1 Shifting Curves along Axes

1.12.2 Shifting or Translating Curves along Axes

1.12.3 Stretching a Graph

1.12.4 Graphing Quadratics Using Patterns

**1.13 Manipulating Graphs: Symmetry and Reflections **

1.13.1 Determining Symmetry

1.13.2 Reflections

1.13.3 Reflecting Specific Functions

**1.14 Quadratic Functions: Basics **

1.14.1 Deconstructing the Graph of a Quadratic Function

1.14.2 Nice-Looking Parabolas

1.14.3 Using Discriminants to Graph Parabolas

1.14.4 Maximum Height in the Real World

**1.15 Quadratic Functions: The Vertex **

1.15.1 Finding the Vertex by Completing the Square

1.15.2 Using the Vertex to Write the Quadratic Equation

1.15.3 Finding the Maximum or Minimum of a Quadratic

1.15.4 Graphing Parabolas

**1.16 Composite Functions **

1.16.1 Using Operations on Functions

1.16.2 Composite Functions

1.16.3 Components of Composite Functions

1.16.4 Finding Functions That Form a Given Composite

1.16.5 Finding the Difference Quotient of a Function

1.16.6 Calculating the Average Rate of Change

**1.17 Rational Functions **

1.17.1 Understanding Rational Functions

1.17.2 Basic Rational Functions

**1.18 Graphing Rational Functions **

1.18.1 Vertical Asymptotes

1.18.2 Horizontal Asymptotes

1.18.3 Graphing Rational Functions

1.18.4 Graphing Rational Functions: More Examples

1.18.5 Oblique Asymptotes

1.18.6 Oblique Asymptotes: Another Example

**1.19 Function Inverses **

1.19.1 Understanding Inverse Functions

1.19.2 The Horizontal Line Test

1.19.3 Are Two Functions Inverses of Each Other?

1.19.4 Graphing the Inverse

**1.20 Finding Function Inverses **

1.20.1 Finding the Inverse of a Function

1.20.2 Finding the Inverse of a Function with Higher Powers