1. (a) \( f(40) = 13 \) tons per week. (b) The amount of garbage produced by a city with population 5,000 is 2 tons per week.
2. (a) \( g(5000) = 50 \) cubic yards. (b) One cubic yard of dirt is needed to cover a 100 square-feet garden.
3. abde
4. abe
5. ab
6. ac
7. (a) \( g(2) = 4. \) (b) \( x = -3. \)
8. (a) \( f(4) = 2. \) (b) \( x = -3. \)
9. (a) \( f(3) = 53. \) (b) \( x = 2. \)
10. (a) \( f(8) = 75. \) (b) \( x = 2 .\)
11. \( f(-2) = 8, f(-1) = 6, f(0) = 4, f(1) = 2, f(2) = 0. \)
12. \( f(-2) = 14, f(-1) = 11, f(0) = 8, f(1) = 5, f(2) = 2. \)
13. \( f(-2) = 49, f(-1) = 18, f(0) = 3, f(1) = 4, f(2) = 21. \)
14. \( f(-2) = 42, f(-1) = 17, f(0) = 4, f(1) = 3, f(2) = 14. \)
15. \( f(-2) = 4, f(-1) = 3+\sqrt{2}, f(0) = 3+\sqrt{3}, f(1) = 5, f(2) = 3+\sqrt{5}. \)
16. \( f(-2) = 4-\sqrt[3]{-4}, f(-1) = 4-\sqrt[3]{-3}, f(0) = 4-\sqrt[3]{-2}, f(1) = 5, f(2) = 4. \)
17. \( f(-2) = 5, f(-1) = \mathrm{DNE}, f(0) = -3, f(1) = -1, f(2) = -1/3. \)
18. \( f(-2) = \mathrm{DNE}, f(-1) = -3, f(0) = -1, f(1) = -1/3, f(2) = 0. \)
19. (a) \( f(0) = 5. \) (b) \( t = -5/3. \)
20. (a) \( g(0) = 6. \) (b) \( p = 3. \)
21. (a) \( f(c) = L. \) (b) \( x = K. \) (c) \( L = (c,t), K = (a,p). \)
22. a—viii, b—vii, c—ii, d—i, e—iv, f—vi, g—iii, h—v.
23. \( \mathrm{Domain} = (2,8], \mathrm{Range} = [6,8). \)
24. \( \mathrm{Domain} = [4,8), \mathrm{Range} = (2,8]. \)
25. \( x \geq 2. \)
26. \( x \geq -3. \)
27. \( x \neq 6. \)
28. \( x \neq 8. \)
29. \( x \neq -1/2. \)
30. \( x \neq 1/4. \)