**3.1 Graphing Basics **

3.1.1 Using the Cartesian System

3.1.2 Thinking Visually

**3.2 Relationships between Two Points **

3.2.1 Finding the Distance between Two Points

3.2.2 Finding the Second Endpoint of a Segment

**3.3 Relationships among Three Points **

3.3.1 Collinearity and Distance

3.3.2 Triangles

**3.4 Circles **

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

3.4.2 Decoding the Circle Formula

3.4.3 Finding the Center and Radius of a Circle

3.4.4 Solving Word Problems Involving Circles

**3.5 Graphing Equations **

3.5.1 Graphing Equations by Locating Points

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

**3.6 Function Basics **

3.6.1 Functions and the Vertical Line Test

3.6.2 Identifying Functions

3.6.3 Function Notation and Finding Function Values

**3.7 Working with Functions **

3.7.1 Determining Intervals Over Which a Function Is Increasing

3.7.2 Evaluating Piecewise-Defined Functions for Given Values

3.7.3 Solving Word Problems Involving Functions

**3.8 Function Domain and Range **

3.8.1 Finding the Domain and Range of a Function

3.8.2 Domain and Range: One Explicit Example

3.8.3 Satisfying the Domain of a Function

**3.9 Linear Functions: Slope **

3.9.1 An Introduction to Slope

3.9.2 Finding the Slope of a Line Given Two Points

3.9.3 Interpreting Slope from a Graph

3.9.4 Graphing a Line Using Point and Slope

**3.10 Equations of a Line **

3.10.1 Writing an Equation in Slope-Intercept Form

3.10.2 Writing an Equation Given Two Points

3.10.3 Writing an Equation in Point-Slope Form

3.10.4 Matching a Slope-Intercept Equation with Its Graph

3.10.5 Slope for Parallel and Perpendicular Lines

**3.11 Linear Functions: Applications **

3.11.1 Constructing Linear Function Models of Data

3.11.2 Linear Cost and Revenue Functions

**3.12 Graphing Functions **

3.12.1 Graphing Some Important Functions

3.12.2 Graphing Piecewise-Defined Functions

3.12.3 Matching Equations with Their Graphs

**3.13 The Greatest Integer Function **

3.13.1 The Greatest Integer Function

3.13.2 Graphing the Greatest Integer Function

**3.14 Quadratic Functions: Basics **

3.14.1 Deconstructing the Graph of a Quadratic Function

3.14.2 Nice-Looking Parabolas

3.14.3 Using Discriminants to Graph Parabolas

3.14.4 Maximum Height in the Real World

**3.15 Quadratic Functions: The Vertex **

3.15.1 Finding the Vertex by Completing the Square

3.15.2 Using the Vertex to Write the Quadratic Equation

3.15.3 Finding the Maximum or Minimum of a Quadratic

3.15.4 Graphing Parabolas

**3.16 Manipulating Graphs: Shifts and Stretches **

3.16.1 Shifting Curves along Axes

3.16.2 Shifting or Translating Curves along Axes

3.16.3 Stretching a Graph

3.16.4 Graphing Quadratics Using Patterns

**3.17 Manipulating Graphs: Symmetry and Reflections **

3.17.1 Determining Symmetry

3.17.2 Reflections

3.17.3 Reflecting Specific Functions

**3.18 Composite Functions **

3.18.1 Using Operations on Functions

3.18.2 Composite Functions

3.18.3 Components of Composite Functions

3.18.4 Finding Functions That Form a Given Composite

3.18.5 Finding the Difference Quotient of a Function

3.18.6 Calculating the Average Rate of Change