This lesson covers chapters 1.1 through 1.5 in the Calculus I textbook, focusing on notation for intervals and functions, analyzing inequalities and absolute value expressions, adopting concepts of analytic geometry including domain and range, and graphing common functions like straight lines, quadratics, square roots, and absolute value functions. The lesson provides examples and results for students to check their work in graphing these basic functions.

1. Mathematics 1000 Lesson #1 Calculus I

2. Objectives of this lesson Distinguish notation for intervals and functions. Analyze inequalities, absolute value, and absolute value inequalities. Adopt basic analytic geometry concepts. Adopt concepts of domain and range of a function.

3. Objectives cont’d Perform the generalized graphing of common functions such as: Straight line Quadratic Square root Absolute-value

4. Notation for Intervals This lectures covers pages 1 – 11, sections 1.1 – 1.5. o o a b

5. Inequalities 1. 2. 3. 4.

6. Absolute value

7. Absolute value inequalities Example #1 if and only if which implies

8. Some Analytic Geometry B A

9. Analytic result

10. Domain and range of a function Now for a short video: http://www.youtube.com/watch?v=Ie_TExJdCQw

11. Graphing “common” functions Common Steps to Produce Graph 1. Recognize function type and recall general shape. 2. Make note of Domain. 3. Create table of values. 4. Plot points and join appropriately.

12. Straight line plot General Form: Example:

13. Example #1 result Does your plot look like this? What did you do wrong or right?

14. Quadratic function plot General Form: Example:

15. Example #2 result Does your plot look like this? What did you do wrong or right?

16. Square-root function plot General Form: Example:

17. Example #3 result Does your plot look like this? What did you do wrong or right?

18. Absolute value function plot General Form: Example:

19. Example #4 result Does your plot look like this? What did you do wrong or right?