## New Functions from Old:Scaled and Shifted Functions exercises to accompany Calculus Applied to the Real World

Index of On-Line Topics
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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) = 1x + 2 2 f(x) = 1x - 1
Graph of f(x) (Select One)

 3 f(x) = (x+1)2 4 f(x) = (x+3)2

Graph of f(x) (Select One)

 5 f(x) = 1x - 1 - 1 6 f(x) = 1x + 1 + 2

Graph of f(x) (Select One)

 7 f(x) = (x2)2 + 1 8 f(x) = (x2)2 2

Graph of f(x) (Select One)

 9 f(x) = |2x + 2| 10 f(x) = 2|x + 2|

Graph of f(x) (Select One)

 11 f(x) = 2|x + 1| 12 f(x) = |2x + 1|

Graph of f(x) (Select One)

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.")

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?

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?