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FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPS: Skills Practice • 99

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FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPS

I. Analyzing Absolute Value Functions

A. Graph the function that represents each problem situation.

1. A jewelry company is making 16-inch bead necklaces. The specifi cations allow for a diff erence of 0.5 inch. The function f(x) 5 |x 2 16| represents the diff erence between the necklaces manufactured and the specifi cations. Graph the function. What necklace lengths meet the specifi cations?

Length of Necklace (inches)

Diff

eren

ce in

Len

gth

(inch

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

2. Julian is cutting lengths of rope for a class project. Each rope length should be 10 inches long. The specifi cations allow for a diff erence of 1 inch. The function f(x) 5 |x 2 10| represents the diff erence between the rope lengths cut and the specifi cations. Graph the function. What rope lengths meet the specifi cations?

Rope Lengths (inches)

Diff

eren

ce in

Len

gth

(inch

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

Skills PracticeName Date

IM2_SP_M03_T01.indd 99IM2_SP_M03_T01.indd 99 24/05/18 1:34 PM24/05/18 1:34 PM

102 • MODULE 3: Exploring Functions

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II. Solving Absolute Value Equations and InequalitiesA. Match each compound inequality to its equivalent absolute value inequality.

1.a. 2 15 , 23x 1 7 , 15 |23x 1 7| # 15b. 23x 1 7 # 215 or 23x 1 7 $ 15 |23x 1 7| . 15c. 215 # 23x 1 7 # 15 |23x 1 7| , 15d. 23x 1 7 , 215 or 23x 1 7 . 15 |23x 1 7| $ 15

2.a. 22 # 6x 2 5 # 2 |6x 2 5| . 2b. 6x 2 5 , 22 or 6x 2 5 . 2 |6x 2 5| $ 2c. 6x 2 5 # 22 or 6x 2 5 $ 2 |6x 2 5| , 2d. 22 , 6x 2 5 , 2 |6x 2 5| # 2

3.a. 211 , 2x 2 10 , 11 |2x 2 10| . 11b. 2x 2 10 # 211 or 2x 2 10 $ 11 |2x 2 10| # 11c. 211 # 2x 2 10 # 11 |2x 2 10| , 11d. 2x 2 10 , 211 or 2x 2 10 . 11 |2x 2 10| $ 11

B. Solve the linear absolute value inequality by rewriting it as an equivalent compound inequality. Then graph your solution on the number line.

1. |x 2 3| $ 4

–6–8–10 –4 –2 0 42 6 8 10

2. 5 . |2x 1 7|

–6–8–10 –4 –2 0 42 6 8 10

3. |3x 2 1| . 11

–6–8–10 –4 –2 0 42 6 8 10

4. |2x 2 8| 2 1 # 3

–6–8–10 –4 –2 0 42 6 8 10



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III. Piecewise FunctionsA. Complete each table. Then, sketch a graph that represents the problem situation.

1. Rosa saved $100 to spend on vacation. For the fi rst 3 days of her vacation she spent $20 each day. Then for the next 2 days, she spent nothing. After those 5 days, she spent $10 each day until her savings were depleted.

Time (days) Savings (dollars)

0

1

2

3

4

5

6

7

8

9

Time (days)

Rosa’s Vacation Spending

Savi

ngs

(dol

lars

)

x

y

40

1 2 30

50

30

20

60

10

4 8 96 75

80

90

70



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Name Date

5. Maria earns money delivering newspapers each morning. For the fi rst 3 days she earns $18 each day. For the next 2 days she takes on an additional route to cover a coworker who is out sick and earns $36 each day. For the next 2 days she returns to her original route and earns $18 each day.

Time (days) Earnings (dollars)

0

1

2

3

4

5

6

7

Time (days)

Maria’s Paper Route

Earn

ings

(dol

lars

)

x

y

72

1 2 30

90

54

36

108

18

4 8 96 75

144

162

126

6. Franco saved $200 to spend at an amusement park while on vacation. For the fi rst 2 days of his vacation he spent $36 each day. Then for the next 2 days, he spent nothing. After those 4 days he stayed 3 more days and spent $40 each day.

Time (days) Savings (dollars)

0

1

2

3

4

5

6

7

Time (days)

Franco’s Vacation Spending

Savi

ngs

(dol

lars

)

x

y

100

0

50

150

1 2 3 4 8 96 75



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B. Write a piecewise function to represent the data shown in each table.

1. x f(x)

0 60

1 55

2 50

3 45

4 45

5 45

6 45

7 43

8 41

9 39

2. x f(x)

0 0

2 3

4 6

6 9

8 12

10 12

12 12

14 18

16 24

18 30



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Name Date

3. A kids bounce house charges $8 for the fi rst hour and $2 for each additional hour of playtime. Write a function that represents the charges for up to 5 hours of playtime.

4. A fundraising company bases the profi t returned to organizations on the total value of products sold. The profi t returned is calculated as follows:

• $100 for sales more than $0 and up to and including $250,

• $225 for sales more than $250 and up to and including $500,

• $350 for sales more than $500 and up to and including $750, and

• $475 for sales more than $750 and up to and including $1000.

IV. Step FunctionsA. Write a step function to represent each problem situation.

1. To encourage quality and minimize defects, a manufacturer pays his employees a bonus based on the value of defective merchandise produced. The less defective merchandise produced, the greater the employee's bonus. The bonuses are calculated as follows:

• $50 for more than $0 and up to and including $100 of defective merchandise,

• $30 for more than $100 and up to and including $200 of defective merchandise,

• $10 for more than $200 and up to and including $300 of defective merchandise, and

• $0 for more than $300 of defective merchandise.

2. A jewelry store off ers reward coupons to its customers. A $2 reward coupon is awarded for each $20 spent. Write a function that represents the value of reward coupons awarded for up to $100 spent.


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