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. $$f(-2) = 4-\sqrt{-4}, f(-1) = 4-\sqrt{-3}, f(0) = 4-\sqrt{-2}, f(1) = 5, f(2) = 4.$$
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. $$x \neq 1/4.$$