Chapter 1 Linear Functions Table of Contents 1.1 Solving Linear Equations 1.2 Using Data to Create...

Chapter 1Linear Functions Table of Contents1.1 Solving Linear Equations 1.2 Using Data to Create Scatterplots 1.3 Fundamentals of Graphing and Slope1.4 Intercepts and Graphing1.5 Finding Equations of Lines1.6 Finding Linear Models1.7 Functions and Function Notation

You plan to purchase custom printed lunch coolers for your school staff. If you order 50 or more lunch coolers, there will be a $45 setup fee and each lunch cooler will cost $3.

a. Write an equation for the total cost, C, in dollars for purchasing L lunch coolers.

b. How much would 75 lunch coolers cost?

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c. How many lunch coolers can you purchase with a budget of $400?

1.1-1

45 3C L

3 Back to Table of Contents

Golf Carts To Go sells refurbished golf carts in south Florida. The company has fixed costs of $26,000 per month for rent, salary and utilities. They can buy used carts and refurbish them for an average of $1,400 each. They sell the carts for an average price of $2500 each. Golf Carts To Go can only refurbish 55 carts a month.

a. Write an equation for the monthly cost of refurbishing n carts.



b. Write an equation for the monthly revenue from selling golf carts.



c. Write an equation for the monthly profit the company makes if they refurbish and sell n carts.


d. What is the profit of refurbishing and selling 25 golf carts?

1.1-2

2500R n


26,000 1400C n 1100 26,000P n

e. How many golf carts does the company have to refurbish and sell to earn $20,000 profit?

1.1-28

26,000 1400C n 2500R n 1100 26,000P n

Back to Table of Contents

Golf Carts To Go can only refurbish 55 carts a month.

f. How many golf carts does the company have to refurbish and sell to earn $40,000 profit?

1.1-29

26,000 1400C n 2500R n 1100 26,000P n


Solve


1 32

4 8x 2 7

( 4) 55 10x x

Solve


6 3(4.1 2) 3 13.2p p p

Solve for p. Solve for r.

1.1-4

R pq 21

3H m r

12

Solve for x.

1.1-4

d ax c


Create a scatterplot of the data given in the table.The percent of adults aged 20 years and over in the UnitedStates who are considered obeseare given in the table.

Source: CDC 2008 National Health Interview Survey.

1.2-1

Year Percent2004 24.52005 25.42006 26.42007 26.72008 26.8


a. Using the scatterplot of the obesity data from before, draw an “eyeball best fit” line through the data.


1.2-1

b. Using your eyeball best-fit line, make a prediction for the percentage of adults in the United States who were considered obese in 2010.


Use the graph to answer the following questions a. Estimate the vertical

intercept.

b. Estimate the horizontal intercept.

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Contents

Use the graph to answer the following questions

c. Estimate the input value that makes the output of this

graph equal 3.

d. Estimate the output value of this graph when the input value is .

1.2-3

2


Determine a reasonable domain and range for the graphical model found for the obesity data.


The percentage of students in twelfth grade who report smoking daily is given in the table. Source: www.monitoringthefuture.org

a. Create a scatterplot for these data and draw an “eyeball best fit” line through the data.

1.2-5

Year Percent2000 20.62001 19.02002 16.92003 15.82004 15.62005 13.62006 12.2


Answer: t = years since 2000. P = percent of twelfth grade students who report smoking daily.


b. Determine the vertical intercept for this model. Explain its meaning in

this situation.

c. Find a reasonable domain and range for this model.


d. According to your graphical model, what percentage of twelfth grade students reported smoking daily in 2007?


Graph the equations by creating a table of values and plotting the points.a. b.


2 6y x 2 5y x

An equation for the total cost, C, in dollars for purchasing L lunch coolers is .

a. Create a table of points that satisfy this equation.


45 3C L


b. Create a graph for the equation using your points. Label your graph with units.

1.3-2

45 3C L


Use the graph to estimate the slope of the line and determine if the line is increasing or decreasing.


Find the slope of the line passing through the points given in the table.

1.3-4

x y

5

8 6

4 24

1 16.5

1.5


Determine if the points given in the table all lie on a line.a.


x y

6 11

10 16

12 18.5

22 31

Determine if the points given in the table all lie on a line.b.

1.3-5

x y

5.4

2 3.4

4 2.8

8 1

3


Find the slope and y-intercept of the following lines.a. b.

1.3-6

6 4y x 1 3

5 10y x


Find the slope and y-intercept of the following lines.c.

1.3-6

4 3 15x y


Find the slope of the model and explain its meaning in the given situation.a. Let be the total cost in dollars to produce p pizzas a day at a local pizzeria.

1.3-7

4.5 1200C p


Find the slope of the model and explain its meaning in the given situation.b. Let be the percentage of adults aged 18 years old and over in the United States that have been diagnosed with diabetes, t years since 2000. Source: CDC.

1.3-7

0.28 5.95D t


Sketch the graph of the following lines. Label the vertical intercept.

a. b.

1.3-8

36

4y x 2 7y x


Rewrite the following equations in general form.

a. b.

1.4-1

3 15y x 1 3

5 8y x


Find the vertical and horizontal intercepts, and explain their meaning in the given situation.

Let be the percentage of adults aged 18 years old and over in the United States that have been diagnosed with diabetes, t years since 2000. Source: CDC.

1.4-2

0.28 5.95D t


Find the horizontal and vertical intercepts of

1.4-3

6 5 42x y


Find the intercepts and graph the line

1.4-4

2 3 18x y


Sketch the graph of the following lines

a.


4x

Sketch the graph of the following lines

b.

1.4-5

1.5y


Write the equation of the line that passes through the points

(4,3) and (20,-17)


A business purchased a production machine in 2005 for $185,000. For tax purposes, the value of the machine in 2011 was $129,500. If the business is using straight line depreciation, write the equation of the line that gives the value of the machine based on the age of the machine in years.


According to www.childtrendsdatabank.org the number of newly diagnosed AIDS cases for adolescents 13-19 years old in the United States was 310 in 2000 and 458 in 2003. Assume that the number of cases is growing at a constant rate, and write an equation to represent this situation.


Use the point slope formula to write the equation of the line that passes through the points and .

1.5-4

(6, 13) (18, 31)


a. Write the equation of the line that passes through the points in the table.

1.5-5

x y

5 13

7 15.8

15 27

18 31.2

47 Back to Table of ContentsBack to Table of

Contents

b. Write the equation of the line shown in the graph.


a. Write the equation of the line that goes through the point

and is perpendicular to the line .

1.5-6

4 23y x ( 12,8)


b. Write the equation of the line that goes through the point (8,11) and is parallel to the line .

1.5-6

5 2 30x y


Using the value of the production machine equation we found earlier, answer the following:

a. What is the slope of the equation? What does it represent in regards to the value of the machine?

b. What is the vertical intercept of the equation? What does it represent in this situation?

1.5-7

9250 185,000v a


Using the value of the production machine equation we found earlier, answer the following:

c. What is the horizontal intercept of the equation? What does it represent in this situation?


9250 185,000v a

Using the AIDS equation found in classroom example 3, answer the following:

a. What is the slope of the equation? What does it mean in this situation?

b. What is the vertical intercept for the equation? What does it represent in this situation?


49.3 310C t

There were 44.1 million major home appliances shipped in the United States in 2007. In 2009 only 36.7 million were shipped. Source: Association of Home Appliance Manufacturers.

a. Write an equation for the number of major home appliances shipped in the US t years since 2000.

b. What is the slope of the equation found in part a? What does it represent?


There were 44.1 million major home appliances shipped in the United States in 2007. In 2009 only 36.7 million were shipped. Source: Association of Home Appliance Manufacturers.

c. What is the vertical intercept for the equation you found in part a? What does it represent?

1.5-9

3.7 70A t


Create a scatter plot on your graphing calculator for the population data for North Carolina given in the table.

Source: Population Division, U.S. Census Bureau

1.6-1

YearPopulation (millions)

2003 8.41

2004 8.52

2005 8.66

2006 8.85

2007 9.04

2008 9.22


Find an equation for a model of the population of North Carolina data given earlier.

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Contents

The total revenue for GE is given in the table.

Source: GE 2008 annual report

a. Find an equation for a model of these data.

1.6-3

YearRevenue (billions $)

2004 1242005 1362006 1522007 1722008 183


The total revenue for GE is given in the table. b. Using your model estimate GE’s revenue

in 2010.

c. What is the slope of your model? What does it mean in regards to GE’s revenue?

d. Determine a reasonable domain and range for the model.

1.6-3

Year Revenue (billions $)

2004 1242005 1362006 1522007 1722008 183

59

14.75 65R t


Determine whether the following descriptions of relations are functions or not.

a. The set

b.

c. Weekly salaries during the mth month of the year.

1.7-1

(2,5), (4,8), (10,8), (20,15)A

Day of weekMonday

Wednesday

Saturday

Monday

Temperature degrees Fahrenheit

90 88 91 93


a. Is the equation a function or not?

b. Is the equation a function or not?

1.7-2

7 20y x

2 24 16y x


c. Does the graph represent a function?


= The height of a toy rocket in feet t second after launch. Interpret the mathematical statement .

1.7-3

( )H t(3) 12H


The population of Wisconsin, in millions, is given in the table.

Source: www.census.gov

Let P(t) be the population of Wisconsin, in millions,

t years since 2000.

a. Find an equation for a model of these data. Write your model in function notation.

b. Determine a reasonable domain and range for your model.

1.7-4

YearPopulation (in millions)

2003 5.472004 5.512005 5.542006 5.572007 5.602008 5.63


The population of Wisconsin, in millions, is given in the table.

Source: www.census.gov

c. Find P(14) and interpret its meaning in regard to the population of Wisconsin.

d. Find when P(t) = 5.75 and interpret its meaning in regard to the population of Wisconsin.

1.7-4

YearPopulation (in millions)

2003 5.472004 5.512005 5.542006 5.572007 5.602008 5.63

65

( ) 0.03 5.39P t t


Let

Find the following.

a.

1.7-5

2( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x

(3)f


Let

Find the following.

b.

1.7-5

2( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x

(5)h


Let

Find the following.

c. x such that

1.7-5

2( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x

( ) 15g x


Use the graph to estimate the following.

a.

b. x such that

1.7-6

(2)f

( ) 5f x


Determine the domain and range of the following functions

a.

b.

1.7-7

( ) 3 7f x x

( ) 8g x


Chapter 1 Linear Functions Table of Contents 1.1 Solving Linear Equations 1.2 Using Data to Create...

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