New Functions from Old:

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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 oddnumbered 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)  =  2x + 2 
11.  f(x)  =  2x + 1  12.  f(x)  =  2x + 1 
Exercises 13 through 22 involve modifications of the graph of f(x) = x^{2}. 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 + x^{2}  Answer for 17  18. n(x) = x^{2} 1  
19. r(x) = 3x^{2}  Answer for 19 
 
21. t(x) = 2(x1)^{2} 1  Answer for 21  22. u(x) = 0.5(x + 2)^{2} 
Exercises 2330 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) =2x + 2  Answer for 29  30. r(x) =23x + 1 
In Exercises 3140, 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 OnLine Topics Text for This Topic Everything for Calculus Everything for Finite Math Everything for Finite Math & Calculus Utility: Function Evaluator & Grapher 