1. MATH 105 Section 28 Instructor : Hyosang Kang

2. Lesson Plan Review section 1.1 Team guidelines Homework problem Section 1.2 Assignment

3. Function A function is a rule which takes certain numbers as inputs and assigns to each input number exactly one output number.

4. Rule of Four Words, Tables, Graphs, and Formulas A function can be described using words, data in a table, points on a graph, or a formula.

5. Example 1 (Word) Crickets chirp at a rate that increases as the temperature. The temperature is the number of times a cricket chirps in 15 seconds (1/4 minute) plus 40.

6. Example 1 (Table) R, chirp rate (chirps/minute)T, predicted temperature 2045 4050 6055 8060 10065 12070 14075 16080

7. Example 1 (Graph)

8. Example 1 (Formula) T=1/4R+40 T: temperature, R: chirp rate

9. Function notation To indicate that a quantity Q is a function of a quantity t, we abbreviate Q is a function of t to Q equals “f of t” and, using function notation, to Q=f(t)

10. Vertical Line Test If there is a vertical line which intersects a graph in more than one point, then the graph does not represent a function.

11. Team Guidelines How to make a group? Decide the roles ( Scribe, Clarifier, Reporter, Manager ) First meeting time and place

12. Rate of Change (1) The average rate of change, or rate of change, of Q with respect to t over an interval is ‘Changes in Q’ rate of change = ----------- ‘Changes in t’

13. Rate of Change (2) If Q=f(t), then it is equal to say f(b) - f(a) ---------- b – a a: initial value of t, b: final value of t

15. Worksheet 1.2 Omit ‘per minute’ in problem 2 Find the rate of changes of functions, represented by the table E, F, and G, on each intervals Use y = f(x)

16. Worksheet 1.2

19. Increasing / Decreasing Function If Q=f(t) for t in the interval a≤t≤b, f is an increasing function if the value of f increases as t increases in this interval. f is a decreasing function if the value of f decreases as t increases in this interval.

20. Caution! TRUE: If a function is increasing (decreasing) on an interval, then the average rate of change is positive (negative) on the interval. NOT TRUE: if the average rate of change of a function is positive (negative) on an interval, then the function is increasing (decreasing) on the interval.

21. Example 4 (page 14)

22. Problem 9 (page 15) Do problem 10 if you finished early

23. Problem 9 (page 15)

24. Key words of today The Rule of Four Average rate of change of a function over an interval and its expression The average rate of change and the slope of the secant line joining the point (a,f(a)) and (b,f(b)). Increasing and decreasing functions

25. Assignment Buy & Bring: TI-83 or equivalent Read: section 1.3 and handouts Do: Section 1.1-8,13,15,18 Section 1.2-3,4,6,8,10,15 Team Homework (due 9/16/05): 1.1-18, 1.2-16, 1.3-22, 1.6-6