Practice and Problem-Solving Exercises

A Practice

See Problem 1.

The cost C, in dollars, for pencils is a function of the number n of pencils purchased. The length L of a pencil, in inches, is a function of the time t, in seconds, it has been sharpened. Graph the function shown by each table below. Tell whether the function is linear or nonlinear.

6. Pencil Cost

   Number of Pencils, n	6	12	18	24	30
   Cost, C	$1	$2	$3	$4	$5

7. Pencil Sharpening

   Time (s), t	0	3	6	9	12	15
   Length (in.), L	7.5	7.5	7.5	7.5	7.4	7.3

Graph the function shown by each table. Tell whether the function is linear or nonlinear.

8. x	y
   0	5
   1	5
   2	5
   3	5

9. x	y
   0	− 4 negative 4
   1	− 3 negative 3
   2	0
   3	5

10. x	y
    0	0
    1	1
    2	− 5 negative 5
    3	8

11. x	y
    0	0
    1	3
    2	6
    3	9

    See Problem 2.

12. For the diagram below, the table gives the total number of small triangles y in figure number x. What pattern can you use to complete the table? Represent the relationship using words, an equation, and a graph.

    

    Figure Number, x	Total Small Triangles, y	Ordered Pair (x, y)
    1	3	(1, 3)
    2	12	(2, 12)
    3	27	(3, 27)
    4	□ white square	□ white square
    5	□ white square	□ white square

See Problem 3.

Each set of ordered pairs represents a function. Write a rule that represents the function.

13. (0, 0), (1, 4), (2, 16), (3, 36), (4, 64)
14. ( 1 , 2 3 ) , ( 2 , 4 9 ) , ( 3 , 8 27 ) , ( 4 , 16 81 ) , ( 5 , 32 243 ) open . 1 comma , 2 thirds . close . comma . open . 2 comma , 4 ninths . close . comma . open . 3 comma , 8 twenty sevenths . close . comma . open . 4 comma , 16 over 81 . close . comma . open . 5 comma , 32 over 243 . close
15. (1, 2), (2, 16), (3, 54), (4, 128), (5, 250)
16. (0, 0), (1, 0.5), (2, 2), (3, 4.5), (4, 8)

B Apply

17. Writing The rule v = 4 3 π r 3 v equals , 4 thirds , pi , r cubed  gives the volume V of a sphere as a function of its radius r. Identify the independent and dependent variables in this relationship. Explain your reasoning.
18. Open-Ended Write a rule for a nonlinear function such that y is negative when x = 1, positive when x = 2, negative when x = 3, positive when x = 4, and so on.

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