Chapter 9.5 Comparing Functions.notebook

1

April 14, 2017

Apr 16­8:21 AM

Bellwork:

1) Write the equation of the line that passes thought the points (1, 4) and (3, 8).

2) Identify which lines are parallel: y = ­1/3x; y = 3x + 2; y = ­1/3x ­ 6; y = 3

Which model best represents the following data:

3) (­1, 3), (0, 0), (1,3), (2, 12)

4) (­2, 11), (­1, 9), (0, 7), (1, 5), (2, 3)

Apr 16­8:26 AM

Homework Questions???

Apr 16­8:27 AM

Chapter 9.5 Comparing Functions

Compare functions in different representations.

Estimate and compare rates of change.

Apr 16­8:27 AM

We can compare functions to each other.

Comparing linear functions (look at slopes and y­intercepts and interpreting the meaning of the those values)

1) Sonia and Jackie each bake and sell cookies after school, and they each charge a delivery fee. The revenue for the sales of various numbers of cookies is shown. Compare the girls' prices by finding and interpreting the slopes and y­intercepts.

Sonia's Revenue

Cookies Sold Revenue ($)

24 11.00

48 17.00

72 23.00

96 29.00

120 35.00

144 41.00

168 47.00

Jackie's Revenue

20 40 60 80 100

481216202428322640

Sonia's Slope: Jackie's Slope:

Sonia's y­intercept: Jackie's y­intercept:

Interpret:

Cookies Sold

Revenue ($)

Apr 16­8:27 AM

2) Dave and Arturo each deposit money into their checking accounts weekly. Their account information for the past several weeks is shown. Compare the accounts by finding and interpreting slopes and y­intercepts.

Dave's Account

Weeks Account Balance ($)

0 30

1 42

2 54

3 66

Arturo's Account

1 2 3 4 5

8

16

24

32

40

48

Dave's Slope: Arturo's Slope:

Dave's y­intercept: Arturo's y­intercept:

Interpret:

Weeks

Account Balance ($)

Apr 14­12:40 PM

Average Rate of Change: Slope of the line through the points (x1, y1) and (x2, y2). For the interval [x1, x2].

Let's look at another problem to find Rates of Change.

Michael is studying population changes in two types of birds living on an island. Compare the populations by finding and interpreting the average rates of change over the interval [0, 18].

Bird BTime

(months)Population (thousands)

0 3.66 5.112 7.218 10.27

Bird A

2 4 6 8 10

8.0

Time(months)

Population (thousands)

8.28.48.68.89.09.29.49.6

12 14 16 18 20

Average Rate of Change over the interval [0, 18]

Bird A: Bird B

Interpret:

Chapter 9.5 Comparing Functions.notebook

2

April 14, 2017

Apr 14­12:41 PM

Compare Different Types of Functions:

3) Graph the three functions using the domain of ­2, ­1, 0, 1, 2.

Function 1 Function 2 Function 3y = ­x2 +4x ­ 2 y = 2x ­ 3 y = ¼(4)x

a. Calculate the rate of change for each graph over [­2, 1].

b. Which function has the greatest rate of change over that interval?

Apr 14­12:42 PM

Compare Different Types of Functions:

4) Graph the three functions using the domain of ­2, ­1, 0, 1, 2.

Function 1 Function 2 Function 3y = 2x2 ­ 3 y = 2x y = 2x + 3

a. Calculate the rate of change for each graph over [0, 3].

b. Which function has the greatest rate of change over that interval?

Apr 16­8:50 AM

Homework:

Practice 9.5 WS

Apr 14­4:12 PM

Apr 16­9:43 AM