New Functions from Old:
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Index of On-Line Topics Text for This Topic Everything for Calculus Everything for Finite Math Everything for Finite Math & Calculus Utility: Function Evaluator & Grapher |
In each of the following, first sketch the select the graph of the given function, then select the graph below that corresponds to your sketch.
Note: Clicking on a graphic gives feedback for odd-numbered exercises only.
1. | f(x) | = | x + 2 |
2. | f(x) | = | x - 1 |
3. | f(x) | = | (x+1)2 | 4. | f(x) | = | (x+3)2 |
5. | f(x) | = | x - 1 | - | 1 | 6. | f(x) | = | x + 1 | + | 2 |
7. | f(x) | = | (x2)2 + 1 | 8. | f(x) | = | (x2)2 2 |
9. | f(x) | = | |2x + 2| | 10. | f(x) | = | 2|x + 2| |
11. | f(x) | = | 2|x + 1| | 12. | f(x) | = | |2x + 1| |
Exercises 13 through 22 involve modifications of the graph of f(x) = x2. In each case, sketch the graph and say what scaling or shifting procedure was used. (For instance "the graph was shifted 10 units to the right.")
13. g(x) = (x 1)2 | Answer for 13 | 14. h(x) = (2x)2 | |||||||
| Answer for 15 | 16. l(x) = (x + 2)2 | |||||||
17. m(x) = 2 + x2 | Answer for 17 | 18. n(x) = x2 1 | |||||||
19. r(x) = 3x2 | Answer for 19 |
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21. t(x) = 2(x1)2 1 | Answer for 21 | 22. u(x) = 0.5(x + 2)2 |
Exercises 23-30 are based on the functions f(x) = (x)1/2 and g(x) = |x|. Sketch their graphs, and say what scaling or shifting procedure was used.
23. h(x) = (x 2)1/2 + 1 | Answer for 23 | 24. h(x) = (x 1)1/2 + 1 |
25. h(x) = [ (x 2)]1/2 + 1 | Answer for 25 | 26. h(x) = 1 (x 1)1/2 |
27. m(x) = |2x + 2| | Answer for 27 | 28. m(x) = |2 x| |
29. r(x) =2|x + 2| | Answer for 29 | 30. r(x) =2|3x + 1| |
In Exercises 31-40, give an equation for the function f whose graph is given.
Applications
40. Cost Functions Suppose that fixed costs were to rise by $10,000. Exactly how would the new cost function be related to C? How would their graphs be related?
41. Cost Functions Suppose that D(x) represents the cost to manufacture x more than 1,000 items. Exactly how are D and C related? How are their graphs related?
Answer
42. Cost Functions Suppose that D(x) represents the cost, in thousands of dollars, to manufacture x items. Exactly how are D and C related? How are their graphs related?
43. Cost Functions Suppose that D(u) represent the cost to manufacture u hundreds of items. Exactly how are D and C related? How are their graphs related?
Answer
New Functions from Old:
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Index of On-Line Topics Text for This Topic Everything for Calculus Everything for Finite Math Everything for Finite Math & Calculus Utility: Function Evaluator & Grapher |