19. Think About a Plan Concrete forming tubes are used as molds for cylindrical concrete supports. The volume V of a tube is the product of its length l and the area A of its circular base. You can make 2 3 ft 3 2 thirds , ft cubed  of cement per bag. Write a rule to find the number of bags of cement needed to fill a tube 4 ft long as a function of its radius r. How many bags are needed to fill a tube with a 4-in. radius? A 5-in. radius? A 6-in. radius?

    

    • What is a rule for the volume V of any tube?
    • What operation do you use to find the number of bags needed for a given volume?

20. Fountain A designer wants to make a circular fountain inside a square of grass as shown below. What is a rule for the area A of the grass as a function of r?

    

C Challenge

21. Reasoning What is a rule for the function represented by ( 0 , 2 19 ) , ( 1 , 1 2 19 ) , ( 2 , 4 2 19 ) , ( 3 , 9 2 19 ) , ( 4 , 16 2 19 ) ,  and  ( 5 , 25 2 19 ) ? open . 0 comma , 2 nineteenths . close . comma . open . 1 comma 1 , and 2 nineteenths . close . comma . open . 2 comma 4 , and 2 nineteenths . close . comma . open . 3 comma 9 , and 2 nineteenths . close . comma . open . 4 comma 16 , and 2 nineteenths . close . comma , and . open . 5 comma 25 , and 2 nineteenths . close . question mark  Explain your reasoning.
22. Reasoning A certain function fits the following description: As the value of x increases by 1 each time, the value of y continually decreases by a smaller amount each time, and never reaches a value as low as 1. Is this function linear or nonlinear? Explain your reasoning.

Standardized Test Prep

SAT/ACT

23. The ordered pairs ( − 2 , 1 ) , ( − 1 , − 2 ) , ( 0 , − 3 ) , ( 1 , − 2 ) , open negative 2 comma 1 close comma open negative 1 comma negative 2 close comma open 0 comma negative 3 close comma open 1 comma negative 2 close comma  and (2, 1) represent a function. Which rule could represent the function?

    1. y = − 3 x − 5 y equals negative 3 x minus 5
    2. y = x 2 − 3 y equals , x squared , minus 3
    3. y = x + 3 y equals x plus 3
    4. y = x 2 + 5 y equals , x squared , plus 5
24. You are making a model of the library. The floor plans for the library and the plans for your model are shown. What is the value of x?

    

    6. 1.4 in.
    7. 23.2 in.
    8. 2.8 in.
    9. 437.5 in.

Short Response

25. A 15-oz can of tomatoes costs $.89, and a 29-oz can costs $1.69. Which can has the lower cost per ounce? Justify your answer.

Mixed Review

See Lesson 4-2.

26. Determine whether the relationship in the table is a function. Then describe the relationship using words, an equation, and a graph.

    x	0	1	2	3
    y	3	5	7	9

Get Ready! To prepare for Lesson 4-4, do Exercises 27–29.

See Lesson 1-2.

Evaluate each expression for x = − 3 , x = 0 , bold italic x equals negative 3 comma bold italic x equals 0 comma  and x = 2.5 . bold italic x equals 2.5 .

27. 7 x − 3 7 x minus 3
28. 1 + 4 x 1 plus 4 x
29. − 2 x 2 negative 2 , x squared

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