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.![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200527/CNX_Precalc_Figure_01_01_201.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200529/CNX_Precalc_Figure_01_01_202.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200530/CNX_Precalc_Figure_01_01_203.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200532/CNX_Precalc_Figure_01_01_204.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200533/CNX_Precalc_Figure_01_01_205.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200535/CNX_Precalc_Figure_01_01_206.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200537/CNX_Precalc_Figure_01_01_207.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200538/CNX_Precalc_Figure_01_01_208.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200539/CNX_Precalc_Figure_01_01_209.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200541/CNX_Precalc_Figure_01_01_210.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200543/CNX_Precalc_Figure_01_01_211.jpg)
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200544/CNX_Precalc_Figure_01_01_212.jpg)
a. Evaluate . b. Solve for .
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200546/CNX_Precalc_Figure_01_01_213.jpg)
a. Evaluate . b. Solve for .
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200547/CNX_Precalc_Figure_01_01_214.jpg)
a. Evaluate . b. Solve for .
![Graph of relation.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200549/CNX_Precalc_Figure_01_01_215.jpg)
![Graph of a circle.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200550/CNX_Precalc_Figure_01_01_216.jpg)
![Graph of a parabola.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200551/CNX_Precalc_Figure_01_01_232.jpg)
![Graph of a rotated cubic function.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200553/CNX_Precalc_Figure_01_01_217.jpg)
![Graph of half of 1/x.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200554/CNX_Precalc_Figure_01_01_218.jpg)
![Graph of a one-to-one function.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200555/CNX_Precalc_Figure_01_01_233.jpg)
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.