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

2. Figure 1.1: The Cartesian Plane

3. Figure 1.2: Coordinates on the Cartesian Plane

4. Figure 1.5: Pythagorean Theorem

5. Figure 1.6: The Distance Formula

6. Figure 1.10: The Midpoint Formula

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

8. Figure 1.17: Intercepts of a Graph

9. Finding Intercepts

10. Figure 1.20: Standard Form of the Equation of a Circle

11. General Form of the Equation of a Circle

12. Figure 1.23: Points of Intersection

13. 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)

14. Figure 1.30: Graphs of Mathematical Models

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

16. Figure 1.32

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

18. Point-Slope Form of the Equation of a Line

19. Figure 1.40: Linear Extrapolation and Interpolation

20. Equations of Lines

21. Parallel and Perpendicular Lines

22. Definition of Function, Figure 1.43

23. Figure 1.47: Definition of Composite Function

24. Figure 1.48: Definition of Inverse Function

25. Figure 1.51

26. Definition of the Limit of a Function

27. Properties of Limits

28. Operations with Limits

29. The Limit of a Polynomial Function

30. The Replacement Theorem

31. Existence of a Limit

32. Figure 1.60, Figure 1.61: Definition of Continuity

33. Continuity of Polynomial and Rational Functions

34. Definition of Continuity on a Closed Interval

35. Figure 1.66: Greatest Integer Function

36. Order of Operations

37. Solving Equations