Write the slope and y-intercept of each equation.

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L1S1

1) y = –5x + 6

11) y = 8x – 5

9) y = –4x + 7

7) y = 7x + 2

5) y = 5x – 3

3) y = –2x – 4

2) y = 3x – 2

12) y = 9x + 3

10) y = –6x – 8

8) y = –x + 6

6) y = –3x – 9

4) y = 8x + 1

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Course 3 • Chapter 4 Functions 63

Example 1The Student Council is hiring a DJ for the school dance. The first DJ charges $25 an hour. The second DJ’s fees areshown in the graph. Compare the functions for each DJ bycomparing the fees.

Compare the rates of change.

The first DJ charges $25 an hour. To find the second DJ’s fees, choose two points on the line and find the rate of change between them.

Change in hours

−−−−−−−−−− Change in fee

= 3 - 0 −−−− 2 - 0

or 15

The second DJ charges $15 per hour. Since 15 < 25, thesecond DJ charges less per hour than the first DJ.

Exercises

1. Melanie charges $7.50 an hour to babysit.The table shows how much Luisa chargesfor babysitting. Compare the functions bycomparing their rates of change.

2. Tom and Lisa each spent an afternoon biking onneighborhood trails. The distance y Tom traveled can berepresented by the function y = 11x. The graph showsLisa’s distance.

Lesson 5 ReteachConstruct Functions

The initial value of a function is the corresponding y-value when x equals 0. You can fi nd the initial value of a function from tables, graphs, and words.

Number of Hours

Cost of Babysitting ($)

1 82 163 24

Fee

($)

20

10

30

40

1 2 3 4 5Number of Hours

DJ Fees

Dist

ance

(mi)

63

912151821242730

1 2 3 4 5Number of Hours

Lisa’s Distance

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Course 3 • Chapter 4 Functions 65

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Solve.

1. FUNDRAISING The Pep Club rented a shaved ice machine to sell shaved ice as a fundraiser. They paid an initial fee and then an hourly charge. The table shows the cost per hour. Find and interpret the rate of change and initial value. Assume the relationship between the two quantities is linear.

Number of Hours, x 2 3 4 5

Cost ($), y 30 35 40 45

2. GARDENING Simone planted a tomato plant and measured its height weekly. The total height at 2, 3, 4, and 5 weeks respectively were 13, 16, 19, and 22 inches tall. How tall was the tomato plant when Simone planted it? Assume the relationship is linear.

3. MOVIES Marcus is a member of a theater club. He pays a monthly fee and his movie tickets are then $5 for an unlimited number of movies that month. The graph shows the cost for each month. Find the monthly fee.

1 2 3 4 5

963

121518

Cost

($) 21

242730

Number of Months0

(1, 12.50)

(2, 17.50)

(3, 22.50)

(4, 27.50)

4. PHOTOS The cost of having photos taken includes a sitting fee and $12 for each portrait. The cost of 3, 6, and 9 photos respectively is $51, $87, and $123. What is the sitting fee?

Lesson 6 Homework PracticeConstruct Functions

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Course 3 • Chapter 4 Functions 67

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Determine whether each table represents a linear or a nonlinear function. Explain.

1. x 1 2 3 4

y 4 5 6 7

2. x 0 2 4 6

y 2 6 18 38

3. x 4 6.5 9 11.5 14

y 3 8 13 18 23

4. x 1.5 3 4.5 6

y 2 4 8 16

5. The table shows the cost of long distance calls as a function of the number of minutes used. Is the cost a linear or nonlinear function of the number of minutes used? Explain.

Number of Minutes 40 80 120 160 200

Cost ($) 4.00 8.00 12.00 16.00 20.00

6. MINIMUM WAGE The graph shows a state’s minimum wage from 2005 to 2012. Would you describe the yearly increase as linear or nonlinear? Explain your reasoning.

2005 2006 2007 2008 2009 2010 2011 20120

$5.00

$6.00

$7.00

$8.00

Year

Hour

ly W

age

Washington's Minimum Wage

$7.63$7.35$7.16$7.01$6.90

$6.72$6.50

$5.70

Lesson 7 Homework PracticeLinear and Nonlinear Functions

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NAME _____________________________________________ DATE __________________ PERIOD _________

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Course 3 • Chapter 4 Functions 69

Example 1Graph y = -2x2.

x −2x2 y (x, y)-2 −2(2)2 = −8 −8 (−2, −8)-1 −2(-1)2 = −2 −2 (−1, −2) 0 −2(0)2 = 0 0 (0, 0) 1 −2(1)2 = -2 −2 (1, −2) 2 −2(2)2 = −8 −8 (2, -8)

y

x

y = -2x 2

Example 2Graph y = x2 - 3.

x x2 − 3 y (x, y)-2 (−2)2 −3 = 1 1 (−2, 1)-1 (-1)2 −3 = −2 −2 (−1, −2) 0 (0)2 −3 = −3 −3 (0, −3) 1 (1)2 −3 = -2 −2 (1, −2) 2 (2)2 −3 = 1 1 (2, 1)

y

xO

y = x2 -3

ExercisesGraph each function.

1. y = 2x2 2. y = -0.5x2 3. y = x2 - 1

4. y = 2x2 + 4 5. y = -x2 - 3 6. y = -3x2 + 1

Lesson 8 ReteachQuadratic Functions

A quadratic function, such as A = s2, is a function in which the greatest power of the variable is 2. Its graph is U-shaped, opening upward or downward.

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

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f(x) = x2 – 6x + 11 f(x) = –(x + 1)2 + 3 f(x) = x2 + 4x + 1

f(x) = x2 – 2 f(x) = (x – 1)2 + 1

f(x) = –x(x – 4) f(x) = –x2 – 4x – 2

x

y

1 2 3 4 5-1-2-3-4-5

5

4

3

2

1

-1

-2

-3

-4

-5

f(x) = 3x2

x

y

3 4 5 6 71 2-1-2-3

5

4

3

2

1

-1

-2

-3

-4

-5

f(x) = x2 – 8x + 16

x

f(x)

x

f(x)

x

f(x)

1

0

–2

2

1

–1

3

2

0

4

3

1

5

4

2

x

f(x)

x

f(x)

x

f(x)

–2

–3

0

–3

–4

–1

–1

–2

1

0

–1

2

1

0

3

x

f(x)

x

f(x)

x

f(x)

–4

–2

2

–3

–1

3

–2

0

4

–1

1

5

0

2

6

x

y

1 2 3 4 5-1-2-3-4-5

7

6

5

4

3

1

2

-1

-2

-3

x

y

1 2 3 4 5-1-2-3-4-5

5

4

3

2

1

-1

-2

-3

-4

-5

x

y

3 4 5 6 71 2-1-2-3

7

6

5

4

3

2

1

-1

-2

-3

x

y

1 2 3 4 5-1-2-3-4-5-1

-2

-3

-4

-5

5

4

3

2

1

x

y

1 2 3 4 5-1-2-3-4-5

15

12

9

6

3

-3

-6

-9

-12

-15

x

y

1 2 3 4 5-1-2-3-4-5

3

5

4

2

1

-1

-2

-3

-4

-5

x

y

3 4 5 6 71 2-1-2-3

5

4

3

2

1

-1

-2

-3

-4

-5

Printable Math Worksheets @ www.mathworksheets4kids.com

1) 2) 3)

4) 5)

7) 8) 9)

6)

Score :Name :

Sheet 1Function Table

Complete the function table and sketch the graph.