1. Types of Functions, Rates of Change
Lesson 1.4

2. Constant Functions Consider the table of ordered pairs
The dependent variable is the same
It is constant
The graph is a horizontal line
Month 1 2 3 4 5 6
Rent Paid
$735

3. Linear Functions Consider this set of ordered pairsx y 5 1 8 2 11 3 14 4 17
Consider this set of ordered pairs
If we plot the points and join them we see they lie in a line • • • •

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

5. 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 … in this case, 3

6. Family of Linear Functions
Slope = Rate of Change
y=3x + 5
Slope = m = 3
y-intercept = b = 5

7. Slope and Y-Intercept Considering y = m * x + b
The b is the y-intercept
Where on the y-axis, the line intersects
On your calculator
Go to Y= screen
Enter at Y1 (2/3) * x + 5
Predict what the graph will look like before you specify F2, 6 for standard zoom

8. Slope and Y-Intercept The function y = (2/3) * x + 5
Slope = 2/3 (up to the right)
Y-intercept = 5 •

9. Slope
When slope =
Try y = -7x – 3 (predict the results before you graph)

10. Family of Linear Functions
Calculating slope with two ordered pairs
(X2, Y2) •
(X1, Y1) •
Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

11. 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

12. 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

13. 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

14. 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

15. Warning
Not all functions which appear linear will actually be linear!!
Consider the set of ordered pairs
Graph them
Decide whether graph is linear
Check slope for different pairs t P
67.38 1
69.13 2
70.93 3
72.77 4
74.67 5
76.61 6
78.60

16. Results Graph appears straight But … rate of change is not a constant
slope
67.38 1
69.13
1.75 2
70.93
1.8 3
72.77
1.84 4
74.67
1.9 5
76.61
1.94 6
78.6
1.99

17. Assignment
Lesson 1.4
Page 53
Exercises 1 – 71 EOO