Beginning Algebra, 11th Edition

236 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

For each function ƒ,f ind(a) ( b) and(c) See Example 5.

The graph shows the number of U.S. foreign-born residents (in millions) for selected years.

Use the information in the graph to work Exercises 39– 44. See Example 6.

39.Write the information in the graph as a

set of ordered pairs. Does this set de-

fine a function?

40.Name the function gin Exercise 39.

Give the five years specified in the

domain of g.

41.Find and

42.For what value of xdoes

43.For what value of xdoes?

44.Suppose What does

this tell you in the context of the

application?

A calculator can be thought of as a function machine. We input a number value ( from the

domain), and then, by pressing the appropriate key, we obtain an output value ( from the range).

Use your calculator, follow the directions, and then answer each question.

45.Suppose we enter the value 4 and then take the square root (that is, activate the square

root function,using the key labeled ).

(a)What is the domain value here? (b)What range value is obtained?

46.Enter the value and then activate the squaring function, using the key labeled

(a)What is the domain value here? (b)What range value is obtained?

• 8 x^2.

1 x

g 120052 =35.7.

g 1 x 2 =37.3

g 1 x 2 =19.8?

g 119802 g 120002.

ƒ 1 x 2 =x^3 +x ƒ 1 x 2 =|x| ƒ 1 x 2 =|x+7|

ƒ 1 x 2 = 4 x+ 3 ƒ 1 x 2 =- 3 x+ 5 ƒ 1 x 2 =x^2 - x+ 2

ƒ 122 , ƒ 102 , ƒ 1 - 32.

EXERCISES 47– 52

The table was generated by a graphing calculator.

The expression represents

47.When.

48.What is

49.When.

50.If what is the value of X?

51.The points represented in the table all lie in a straight line.

(a)What is the slope of the line?

(b)What is the y-intercept of the line?

52.Write the function in the form y=mx+b,for the appropriate values of mand b.

ƒ 1 X 2 =2,

Y 1 =2, X =

ƒ 132?

X=3, Y 1 =

Y 1 ƒ 1 X 2.

TECHNOLOGY INSIGHTS

Growth of U.S. Foreign-Born Population

0

10

20

40

30

1970 1980 1990

2007

2000

Year

Population (in millions)

Source: U.S. Census Bureau.

x

y

9.6 14.1

19.8

28.4

37.3

Graph each pair of equations on the same coordinate axes. See Section 3.2.

53. 
    
    
    
    54. 
        
        
        
        55. 
            
            
            
            56. 4 x- 2 y= 8 2 x= 8 - 2 y 2 y=- 4 + 5 x - 2 x+ 3 y= 0
            
            
            
            
        
        
        
        
    
    
    
    

2 x+ 3 y= 12 x+y= 4 - 5 x+ 2 y= 10 2 y=- 3 x

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