Section Exercises
1. What is the difference between a relation and a function? 2. What is the difference between the input and the output of a function? 3. Why does the vertical line test tell us whether the graph of a relation represents a function? 4. How can you determine if a relation is a one-to-one function? 5. Why does the horizontal line test tell us whether the graph of a function is one-to-one? For the following exercises, determine whether the relation represents a function. 6. 7. For the following exercises, determine whether the relation represents as a function of . 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. For the following exercises, evaluate the function at the indicated values . 27. 28. 29. 30. 31. 32. Given the function , evaluate . 33. Given the function , evaluate . 34. Given the function
a. Evaluate . b. Solve .
35. Given the functiona. Evaluate . b. Solve .
36. Given the functiona. Evaluate . b. Solve .
37. Given the functiona. Evaluate . b. Solve .
38. Given the functiona. Evaluate . b. Solve .
39. Consider the relationship .a. Write the relationship as a function . b. Evaluate . c. Solve .
For the following exercises, use the vertical line test to determine which graphs show relations that are functions. 40.
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a. Evaluate . b. Solve for .
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a. Evaluate . b. Solve for .
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a. Evaluate . b. Solve for .
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5 | 10 | 15 | |
3 | 8 | 14 |
5 | 10 | 15 | |
3 | 8 | 8 |
5 | 10 | 10 | |
3 | 8 | 14 |
0 | 74 |
1 | 28 |
2 | 1 |
3 | 53 |
4 | 56 |
5 | 3 |
6 | 36 |
7 | 45 |
8 | 14 |
9 | 47 |
a. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function . b. Explain the meaning of the statement .
89. The number of cubic yards of dirt, , needed to cover a garden with area square feet is given by .a. A garden with area 5000 ft2 requires 50 yd3 of dirt. Express this information in terms of the function . b. Explain the meaning of the statement .
90. Let be the number of ducks in a lake years after 1990. Explain the meaning of each statement:a. b.
91. Let be the height above ground, in feet, of a rocket seconds after launching. Explain the meaning of each statement:a. b.
92. Show that the function is not one-to-one.