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

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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)=
1

x + 2
2. f(x)=
1

x - 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)=
1

x - 1
-1 6. f(x)=
1

x + 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.

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:
Scaled and Shifted Functions
exercises to accompany
Calculus Applied to the Real World

              Return to Main Page
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

Last Updated:January, 1998
Copyright © 1998 StefanWaner and Steven R. Costenoble