Chapter. Algebra Ii

ANSWERS
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Relations and Functions

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Picture or Example

Think About a Plan
Relations and Functions

Complete the vocabulary chart by filling in the missing information. Word or Word Phrase
relation

Definition A relation is a set of ordered pairs of input and output values.

Geometry Suppose you have a box with a 4 3 4-in. square base andvariable height h. The surface area of this box is a function of its height. Write a function to represent the surface area. Evaluate the function for h 5 6.5 in.
22 5

x y

22 1

21 2

0 3

1 4

Understanding the Problem
1. The width of the box is

1. (0, 2), (24, 2), (22, 29)

The height of the box is h inches.

4 4 u inches. The length of the box is u inches. u

2. What is theproblem asking you to determine?
function

A function is a relation where each x-coordinate corresponds to only one y-coordinate.

2. Answers may vary. Sample: {(23, 1), (5, 9), (3, 23)}

A function that gives the surface area of a box with dimensions 4 in. 3 4 in. 3 h in., and the surface area when h 5 6.5 in.

Planning the Solution
3. What is the area of the top of the box? What is thearea of the bottom of the box? 16 in.2; 16 in.2
domain

3. Answers may vary. Sample: The domain is the set of inputs, also called the x-coordinates, of the ordered pairs.

x y

22 24

21 22

0 0

1 2

2 4 4. What is the total area of the top and the bottom of the box? 32 in.2

The domain is {22, 21, 0, 1, 2}.

range

The range is the set of outputs, also called they-coordinates, of the ordered pairs.

4.

5. What is the area of each side of the box? 4h in.2 x y 22 21 23 22 0 21 1 0 2 1 6. What is the total area of the sides of the box? 16h in.2

Answers may vary. Sample: The range is {23, 22, 21, 0, 1}.

function notation

Function notation is a way to write a function rule.

5. Answers may vary. Sample: f (x) 5 22x 1 5, read as “f of x”

Getting anAnswer
7. Write a function to represent the surface area of the box. s(h) 5 16h 1 32

8. Evaluate your function for h 5 6.5 inches. 136 in.2

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Form G
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Practice
Relations and Functions

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Practice (continued)
Relations and Functions

Form G
3/17/09 3:47:26 PM

Thetable shows the number of gold medals won by United States athletes during the Summer Olympics.
U.S. Gold Medals in Summer Olympics Year Gold Medals 1988 36 1992 37 1996 44 2000 40 2004 35 2008 36
Number of gold medals

Domain

Range

Evaluate each function for the given value of x, and write the input x and the output f (x) as an ordered pair.
9. f (x) 5 23x 1 2 for x 5 3 (3, 27) 11. f(x) 5 5x 2 22 for x 5 12 (12, 38)

1988 1992 1996 2000 2004 2008
44 42 40 38 36 34 0 y

35 36 37 40 44

1 10. f (x) 5 2 x 2 1 for x 5 22 (22, 22)
12. f (x) 5 25x 2 3 for x 5 27 (27, 32)
2 5 3 14. f (x) 5 3 x 2 5 for x 5 3 Q 3, 4 5 R

9 13. f (x) 5 4 x 2 15 for x 5 4 (4, 26)

1. Represent the data using each of the following: a. a mapping diagram b. ordered pairs (1988, 36), (1992, 37),(1996, 44), (2000, 40), c. a graph on the coordinate plane (2004, 35), (2008, 36)

Write a function rule to model the cost of renting a truck for one day. Then evaluate the function for the given number of miles.
15. Daily rental: $19.95
x 1988 1992 1996 2000 2004 2008

16. Daily rental: $39.95

Rate per mile: $.50 per mile Miles traveled: 73 miles
f (x) 5 0.5x 1 19.95; $56.45

Rate permile: $.60 per mile Miles traveled: 48 miles
f (x) 5 0.6x 1 39.95; $68.75

2. What is the domain and range of this data set? domain: {1988, 1992, 1996, 2000, 2004, 2008}; range: {35, 36, 37, 40, 44}

Year

Find the domain and range of each relation, and determine whether it is a function.
17.
y 2 O 2 x

Determine whether each relation is a function.
3. Domain 1 0 1 2 3 function...