AA Section 3-1

CHAPTER 3LINEAR FUNCTIONS

Created at http://wordle.net

SECTION 3-1Constant-Increase and Constant-Decrease Situations

WARM-UP

Look at the four graphs on page 139 as such:a. Constant Increase

b. Linear Combinationc. Point-Slope

d. Step Function

1. Name at least two points on each graph.

WARM-UP

2. Give the domain and range of each function

WARM-UP


a. D = Set of whole numbers; R = {n: n = 3, 3.2, 3.4, ...}

WARM-UP



b. D = {A: A = 0, 3, 6}; R = {S: S = 0, 7, 14}

WARM-UP



b. D = {A: A = 0, 3, 6}; R = {S: S = 0, 7, 14}

c. D = {W: W ≥ 0}; R = {L: L ≥ 7}

WARM-UP



b. D = {A: A = 0, 3, 6}; R = {S: S = 0, 7, 14}

c. D = {W: W ≥ 0}; R = {L: L ≥ 7}

d. D = {w: w > 0}; R = {C: C = .33, .55, .77, ...}

Linear Equation:

Linear Equation: Equation that gives a graph of a line

EXAMPLE 1

Matt Mitarnowski sells sports cars. He gets a base salary of $30,000 per year plus 2% of his sales. If Matt’s sales for the

year totaled D dollars, what is his salary S?

EXAMPLE 1



S = 30,000 + .02D

EXAMPLE 1



S = 30,000 + .02D

Let’s look at the table and graph

EXPLORE

Calculate the slope for the situation in Example 1.

EXPLORE


(0, 30,000), (1,000,000, 50,000)

EXPLORE


(0, 30,000), (1,000,000, 50,000)

m =

50, 000 − 30, 0001, 000, 000 − 0

EXPLORE


(0, 30,000), (1,000,000, 50,000)

m =

50, 000 − 30, 0001, 000, 000 − 0

=

20, 0001, 000, 000

EXPLORE


(0, 30,000), (1,000,000, 50,000)

m =

50, 000 − 30, 0001, 000, 000 − 0

=

20, 0001, 000, 000

=

2100

EXPLORE


(0, 30,000), (1,000,000, 50,000)

m =

50, 000 − 30, 0001, 000, 000 − 0

=

20, 0001, 000, 000

=

2100

=150

EXPLORE


(0, 30,000), (1,000,000, 50,000)

m =

50, 000 − 30, 0001, 000, 000 − 0

=

20, 0001, 000, 000

=

2100

= .02 =

150

Slope-intercept Form:

Slope-intercept Form: y = mx + b, where m = slope and b = the y-coordinate of the y-intercept


*In this form, the slope will ALWAYS be with the independent variable, and the y-coordinate of the y-

intercept will ALWAYS be by itself




Linear Function:




Linear Function: A function of the form y = mx + b




Linear Function: A function of the form y = mx + bEuler notation:




Linear Function: A function of the form y = mx + bEuler notation: f(x) = mx + b





Mapping notation:





Mapping notation: f:x mx + b

EXAMPLE 2

Fuzzy Jeff gets an allowance of $15 per week. Whenever his parents pick up a dirty dish he left out, Jeff losts $.30.

a. Write an equation modeling this situation

EXAMPLE 2



A = Allowance; d = Dirty Dishes

EXAMPLE 2




A = 15 - .3d

EXAMPLE 2




A = 15 - .3d

b. Graph the equation

EXAMPLE 2

c. If Jeff gets no allowance, how many dishes did he leave out?

EXAMPLE 2


A = 15 - .3d

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d-15

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d-15-15

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d-15-15

-15 = -.3d

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d-15-15

-15 = -.3d

d = 50

EXAMPLE 2


A = 15 - .3d

0 = 15 - .3d-15-15

-15 = -.3d

d = 50 dishes

Piecewise Linear Graph:

Piecewise Linear Graph: When the rate of change switches from one constant value to another

Piecewise Linear Graph: When the rate of change switches from one constant value to another

*Made up of two or more segments or rays

EXAMPLE 3

The graph below describes Shecky’s weight over the first 16 weeks of his life. Write out an explanation of each piece

of the piecewise linear function.

EXAMPLE 3

EXAMPLE 3

Shecky weighed 9 pounds at birth.

EXAMPLE 3


In his first week alive, he lost one pound.

EXAMPLE 3



Over the next four weeks, Shecky gained a pound a week.

EXAMPLE 3




In the following three weeks, Shecky’s weight stayed the same.

EXAMPLE 3




In the following three weeks, Shecky’s weight stayed the same.

Over the last 8 weeks, Shecky gained half of a pound per week.

HOMEWORK

HOMEWORK

p. 143 #1 - 26

“Fortune favors the brave.” - Publius Terence

AA Section 3-1

Education

Transcript of AA Section 3-1