Intermediate Algebra (11th edition)

10.The total number of airports ( public and private) in the United States during the years
1980 through 2007 can be approximated by the polynomial function defined by

where represents 1980, represents 1981, and so on. Use this function to

approximate the number of airports (to the nearest whole number) in each given year.

(Source:U.S. Bureau of Transportation Statistics.)

(a) 1980 (b) 2000 (c) 2007

11.The amount spent by Americans on foreign travel
during the years 1985 through 2006 can be mod-
eled by the polynomial function defined by

where represents 1985, represents

1986, and so on, and is in billions of dollars.

Use this function to approximate the amount spent

by Americans on foreign travel in each given year.

Round answers to the nearest tenth. (Source:U.S.

Department of Commerce.)

(a) 1985 (b) 2000 (c) 2006

12.The percent of births to unmarried women during the years 1990 through 2007 can be
approximated by the polynomial function defined by

where represents 1990, represents 1991, and so on. Use this function to

approximate the percent (to the nearest tenth) of births to unmarried women in each given

year. (Source:National Center for Health Statistics.)

(a) 1990 (b) 1997 (c) 2007

For each pair of functions, find (a) and (b). See Example 3.

13. ,


14. ,


15. ,


16. ,

Let and. Find each of the following. See Example 4.

27. 28. 29.

30. 31. 32.

33.Construct two functions defined by a polynomial of degree 3, and a polyno-
mial of degree 4. Find Use your answers to decide whether
subtraction of functions is a commutative operation. Explain.

34.Concept Check Find two polynomial functions defined by and such that

1 ƒ+g 21 x 2 = 3 x^3 - x+ 3.

ƒ 1 x 2 g 1 x 2

1 ƒ-g 21 x 2 and 1 g-ƒ 21 x 2.

ƒ 1 x), g 1 x 2 ,

1 g+h2a-

1

4

1 g+h2a- b

1

2

1 g+h2a b

1

3

b

1 g+h2a

1

4

1 g-h 21 - 32 1 g+h 2112 b

1 ƒ+h 21 - 22 1 g+h 21 - 102 1 g-h 21102

1 ƒ-h 21 x 2 1 ƒ+h 21 x 2 1 ƒ-h 21 - 32

1 ƒ+g 21 x 2 1 ƒ-g 21 x 2 1 ƒ+g 2132 1 ƒ-g 21 - 32

ƒ 1 x 2 =x^2 - 9,g 1 x 2 = 2 x, h 1 x 2 =x- 3

ƒ 1 x 2 = 3 x^2 - 9 x+ 10 g 1 x 2 =- 4 x^2 + 2 x+ 12

ƒ 1 x 2 = 4 x 2 + 8 x- 3 g 1 x 2 =- 5 x 2 + 4 x- 9

ƒ 1 x 2 =- 4 x+ 1 g 1 x 2 = 6 x+ 2

ƒ 1 x 2 = 5 x - 10 g 1 x 2 = 3 x+ 7

1 ƒ+g 21 x 2 1 ƒ-g 21 x 2

x= 0 x= 1

ƒ 1 x 2 =0.0077x^3 - 0.1945x^2 +1.857x+26.64,

P 1 x 2

x= 0 x= 1

+2.027x+28.19,

P 1 x 2 =-0.00189x^3 +0.1193x^2

x= 0 x= 1

ƒ 1 x 2 =-2.576x^2 +253.1x+15,160,

SECTION 5.3 Polynomial Functions, Graphs, and Composition 291