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3.6 EXERCISES
Complete the table for the linear function defined by ƒ 1 x 2 =x+2.234 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
NOW TRY ANSWERS
- (a) The
population of Asian-Americans
was 14.9 million in 2006.
(b) 1996
ƒ 120062 =14.9;Applying the Function Concept to PopulationAsian-American populations (in millions) are shown in the table.
EXAMPLE 6
(a)Use the table to write a set of ordered pairs that defines a function ƒ.
If we choose the years as the domain elements and the populations as the range
elements, the information in the table can be written as a set of four ordered pairs. In
set notation, the function ƒis defined as follows.
y-values are
in millions.(b)What is the domain of ƒ? What is the range?
The domain is the set of years, or x-values.
1996, 2000, 2004, 2006
The range is the set of populations, in millions, or y-values.
9.7, 11.2, 13.1, 14.9
(c) Find 1996 and 2004.
We refer to the table or the ordered pairs in part (a).
(d)For what x-value does equal 14.9 million? 11.2 million?
We use the table or the ordered pairs found in part (a).
ƒ 120062 =14.9 million and ƒ 120002 =11.2 million NOW TRY
ƒ 1 x 2
ƒ 119962 =9.7 million and ƒ 120042 = 13.1 million
ƒ 1 2 ƒ 1 2
5 6
5 6
ƒ= 51 1996, 9.7 2 , 1 2000, 11.2 2 , 1 2004, 13.1 2 , 1 2006, 14.9 26
Determine whether each relation isor is nota function. In Exercises 7–12, give the domain
and the range.See Examples 1–3.
7.- 51 3, 7 2 , 1 1, 4 2 , 1 0, - 22 , 1 - 1, - 12 , 1 - 2, 5 26
51 - 4, 3 2 , 1 - 2, 1 2 , 1 0, 5 2 , 1 - 2, - 826
x
02 2
1
2
3
t1 0, 2 2x+ 2 ƒ 1 x 2 1 x, y 25.Describe the graph of function ƒin Exercises 1–3
if the domain is
6.Describe the graph of function ƒin Exercises 1–3
if the domain is the set of real numbers 1 - q, q 2.5 0, 1, 2, 3 6.
1.
2.
3.
4.
OBJECTIVE 6 Apply the function concept in an application.
Year Population (in millions)
1996 9.7
2000 11.2
2004 13.1
2006 14.9
Source: U.S. Census Bureau.NOW TRY
EXERCISE 6
Refer to Example 6.
(a)Find and interpret
this result.
(b)For what x-value does
ƒ 1 x 2 equal 9.7 million?
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