1. Chapter 1 – Introducing Functions Section 1.1 – Defining Functions Definition of a Function Formulas, Tables and Graphs Function Notation Section 1.2 – Using Functions to Model the Real World Abstract and Model Domain and Range Discrete and Continuous One Output for Each Input

2. Exercises from Sections 1.1 and 1.2 1/10 – domain of men’s shoe function 5/10 – domain 6/10 - domain 2/13 – function notation 3/13 – function notation 4/13 – function notation 5/13 – function notation 6/13 – function notation 11/32 – function notation 12/32 – function notation 23/33 – weird function

3. Section 1.3 Watching Functions Values Change pages 17 - 29

4. Section 1.3 – Watching Function Values Change Example 1: women’s shoe size function w(x) = 3x – 21 y = 3x - 21 y (shoe size) depends on x (foot measurement) HOW? foot length increases from 9 inches to 9 1/6 inches (by 1/6) foot length increases from 9 1/6 to 9 1/3 inches (by 1/6) foot length increase from 10 inches to 10 ½ inches (by 1/2) foot length increases by a full inch during the course of a career. What is the change in shoe size when:

5. x (inches) 99 1/69 1/31010 1/2 y=3x-21 (shoe size) 66.57910.5 foot length increases from 9 inches to 9 1/6 inches (by 1/6) foot length increases from 9 1/6 to 9 1/3 inches (by 1/6) foot length increase from 10 inches to 10 ½ inches (by 1/2) foot length increases by a full inch during the course of her career. shoe size increases by 0.5 shoe size increases by 1.5 shoe size increases by 3 Example 1

6. Do you see a pattern? Change in x (inches) 1/6 1/21 Change in y (shoe size) 0.5 1.53 change in y is always 3 times the change in x or change of one unit in x always produces a change of 3 units in y or rate of change is 3 [shoe sizes per 1 inch] women’s shoe size function w(x) = 3x – 21 y = 3x - 21 y (shoe size) depends on x (foot measurement) HOW? Example 1

7. Section 1.3 – Watching Function Values Change Definition (pg 17) The rate of change of y with respect to x is given by: Definition (pg 18) The average rate of change of any function y = f(x) from x = a to x = b is the ratio:

8. women’s shoe size function w(x) = 3x – 21 y = 3x - 21 y (shoe size) depends on x (foot measurement) HOW? Use the definition to determine the average rate of change of the women’s shoe size function for: x from 9 to 9 1/6 x from 9 1/6 to 9 1/3 x from 10 to 10 1/2 x from 9 to 10 x from a to b Example 1

9. Can we see the rate of change on the graph of the women’s shoe size function? Constant Rate of Change = Straight Line Graph Example 1

10. Section 1.3 – Watching Function Values Change Example 2 the area of a square depends on the length of its side A(s) = s 2 HOW? Use the definition to determine the average rate of change of the area function for: s from 1 to 2 s from 2 to 3 s from 3 to 4

11. Use the figures to determine the average rate of change of the area function for: s from 1 to 2 s from 2 to 3 s from 3 to 4 Example 2

12. Can we see the rates of change on the graph of the area function? Example 2 Rate of Change is Changing

13. Section 1.3 – Watching Function Values Change The Shape of a Graph We say a function is increasing if the value of the dependent variable increases as the value of the independent variable increases i.e. as we read the graph from left to right, the y values of points on the graph get larger. i.e. the graph rises as we read left to right

14. Section 1.3 – Watching Function Values Change The Shape of a Graph We say a function is decreasing if the value of the dependent variable decreases as the value of the independent variable increases i.e. as we read the graph from left to right, the y values of points on the graph get smaller. i.e. the graph falls as we read left to right

15. Section 1.3 – Watching Function Values Change The Shape of a Graph What about average rates of change for increasing functions?

16. Section 1.3 – Watching Function Values Change The Shape of a Graph What about average rates of change for decreasing functions?

17. Section 1.3 – Watching Function Values Change The Shape of a Graph We say the graph of a function is concave up if the rates of change increase as we move left to right. We say the graph of a function is concave down if the rates of change decrease as we move left to right.

18. Where is f increasing? Where is f decreasing? Where is graph concave up? Where is graph concave down?

19. Homework: Page 33: #25-31 Page 40: #1, 2 Turn in: 26,27,30, 31 Read and begin work on Lab 1B (pp 46-50) Section 1.3 – Watching Function Values Change