Functions, Graphs, and Limits Chapter 1 Functions, Graphs, and Limits

Figure 1.1: The Cartesian Plane

Figure 1.2: Coordinates on the Cartesian Plane

Figure 1.5: Pythagorean Theorem

Figure 1.6: The Distance Formula

Figure 1.10: The Midpoint Formula

Figure 1.15 and Figure 1.16: (Shortcomings of the Point-Plotting Technique)

Figure 1.17: Intercepts of a Graph

Finding Intercepts

Figure 1.20: Standard Form of the Equation of a Circle

General Form of the Equation of a Circle

Figure 1.23: Points of Intersection

Figure 1. 25 (Supply Curve), Figure 1. 26 (Demand Curve), and Figure 1 Figure 1.25 (Supply Curve), Figure 1.26 (Demand Curve), and Figure 1.27 (Equilibrium Point)

Figure 1.30: Graphs of Mathematical Models

Figure 1.31: The Slope-Intercept Form of the Equation of a Line

Figure 1.32

Figure 1.36: The Slope of a Line Passing Through Two Points

Point-Slope Form of the Equation of a Line

Figure 1.40: Linear Extrapolation and Interpolation

Equations of Lines

Parallel and Perpendicular Lines

Definition of Function, Figure 1.43

Figure 1.47: Definition of Composite Function

Figure 1.48: Definition of Inverse Function

Figure 1.51

Definition of the Limit of a Function

Properties of Limits

Operations with Limits

The Limit of a Polynomial Function

The Replacement Theorem

Existence of a Limit

Figure 1.60, Figure 1.61: Definition of Continuity

Continuity of Polynomial and Rational Functions

Definition of Continuity on a Closed Interval

Figure 1.66: Greatest Integer Function

Order of Operations

Solving Equations