1. Chapter 2.3 Continuity

2. Objectives Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous Functions

3. Learning Target

4. Standard S-ID.6aFit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

5. Overview Understand the meaning of a continuous function. Identify the intervals over which a given function is continuous. Remove removable discontinuities by modifying a function. Apply the Intermediate Value Theorem.

6. Continuous Physical phenomena Particle motion Reaction rates Fit a curve to data Never “connect the dots”

7. Discontinuous Atomic transitions Lasers Black body radiation Ultraviolet “catastrophe” Planck’s Law Einstein – photons

8. Example Continuity

9. Continuity

10. Continuity at a Point

11. Example Continuity at a point Continuity from the right Continuity from the left Two sided continuity

12. Example Greatest Integer Function

13. Discontinuities

14. Continuous vs. Discontinuous continuousremovable

15. Discontinuous removablejump

16. Discontinuous Functions

17. Possible Discontinuities

18. Removing a Discontinuity

22. Continuous Functions

25. Algebraic Combinations

26. Properties of Continuous Functions

27. Composites

28. Composites of Continuous Functions

29. Example

30. The Intermediate Value Theorem

32. Homework P 84: 3-30, multiples of 3, 42, 45, 51, 63