1. Rates of Change
Lesson 1.2

2. Which Is Best? Which roller coaster would you rather ride? Why?
Today we will look at a mathematical explanation for why one is preferable to another.

3. Rate of Change Given function y = 3x + 5 • • • • x y 5 1 8 2 11 3 14 45 1 8 2 11 3 14 4 17
Given function y = 3x + 5 • 6 2 • • •

4. Rate of Change Try calculating for different pairs of (x, y) points5 1 8 2 11 3 14 4 17
Try calculating for different pairs of (x, y) points
You should discover that the rate of change is constant

5. You may need to specify the beginning x value and the increment
Rate of Change
Consider the function
Enter into Y= screen of calculator
View tables on calculator ( Y)
You may need to specify the beginning x value and the increment

6. Rate of Change
As before, determine the rate of change for different sets of ordered pairs x
sqrt(x)
0.00 1
1.00 2
1.41 3
1.73 4
2.00 5
2.24 6
2.45 7
2.65

7. Rate of Change
View Geogebra demo which demonstrates results of the formula below.

8. Rate of Change (NOT a constant)
You should find that the rate of change is changing – NOT a constant.
Contrast to the first function y = 3x + 5

9. Function Defined by a Table
Year
1982
1984
1986
1988
1990
1992
1994
CD sales
5.8 53
150
287
408
662
LP sales
244
205
125 72 12
2.3
1.9
Consider the two functions defined by the table
The independent variable is the year.
Predict whether or not the rate of change is constant
Determine the average rate of change for various pairs of (year, sales) values

10. Increasing, Decreasing Functions
Note that for the CD sales, the rates of change were always positive
For the LP sales, the rates of change were always negative
An increasing function
A decreasing function

11. Increasing, Decreasing Functions
A decreasing function
An increasing function

12. Increasing, Decreasing Functions
Given Q = f ( t )
A function, f is an increasing function if the values of f increase as t increases
The average rate of change > 0
A function, f is an decreasing function if the values of f decrease as t increases
The average rate of change < 0

13. Using TI to Find Rate Of Change
Define a function f(x) 3*x + 5 -> f(x)
We want to define the function and assign it to a function
Use the STO> key

14. Using TI to Find Rate Of Change
Now call the function difquo( a, b ) using two different x values for a and b
For rate of change of a different function, redefine f(x)

15. Assignment
Lesson 1.2
Page 15
Exercises
3, 5, 7, 9, 11, 12, 13, 15, 21