Functions and Graphs ISM: Introductory Mathematical Analysis

doubling the intensity increases the

response by a factor of 23 2.

52. (1) 1 1 (1 0.344)0 1 1 (1) 1

2 2 2

P = − − = − =

(2) 1 1 (1 0.344)1 1 1 (0.656)

2 2

P = − − = − = 0.672

53. a. Domain: 3000, 2900, 2300, 2000

f(2900) = 12, f(3000) = 10

b. Domain: 10, 12, 17, 20

g(10) = 3000, g(17) = 2300

54. a. –18.97

b. –581.77

c. –18.51

55. a. –5.13

b. 2.64

c. –17.43

56. a. 1,997,723.57

b. 1,287,532.35

c. 2,964,247.40

57. a. 7.89

b. 63.85

c. 1.21

Principles in Practice 2.2

1. a. Let n = the number of visits and p(n) be the

premium amount.

p(n) = 125

b. The premiums do not change regardless of

the number of doctor visits.

c. This is a constant function.

2. a. d(t) = 3t2 is a quadratic function.

b. The degree of d(t) = 3t2 is 2.

c. The leading coefficient of d(t) = 3t2 is 3.

3. The price for n pairs of socks is given by

3.5 0 5

( ) 3 5 10

2.75 10

n n

c n n n

n n

≤ ≤ ⎧⎪

= < ≤ ⎨⎪

⎩ <

.

Chapter 2: Functions and Graphs ISM: Introductory Mathematical Analysis

60

4. Think of the bookshelf having 7 slots, from left

to right. You have a choice of 7 books for the

first slot. Once a book has been put in the first

slot, you have 6 choices for which book to put in

the second slot, etc. The number of arrangements

is 7 · 6 · 5 · 4 · 3 · 2 · 1 = 7! = 5040.

Problems 2.2

1. yes

2.

3

( ) 7 3 1 3 7 1,

3 3 3

f x x x x x

+ −

= = + − which is a

polynomial function.

3. no

4. yes

5. yes

6. yes

7. no

8. –4

4

g(x) 4x 4

x

= = , which is a rational function.

9. all real numbers

10. all real numbers

11. all real numbers

12. all x such that 1 ≤ x ≤ 3

13. a. 3

b. 7

14. a. 1

b. 7

15. a. 7

b. 1

16. a. 0

b. 9

17. f(x) = 8

f(2) = 8

f(t + 8) = 8

f (− 17 ) = 8

18. g(x) = x − 3

g(10) = 10 − 3 = 7 = 7

g(3) = 3 – 3 = 0 = 0

g(–3) = –3− 3 = −6 = 6

19. F(10) = 1

F (− 3) = −1

...