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
Español

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. $f(x) = \frac {1}{x + 2}$ 2. $f(x) = \frac {1}{x+ 1}$
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. $f(x) = \frac {1}{x+ 1}-1$ 6. $f(x) = \frac {1}{x+ 1}+2$

Graph of $f(x)$ (Select One)

7. $f(x) = (x-2)^{2} + 1$ 8. $f(x) = (x-2)^{2} - 2$

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 $f(x) = x^2$. 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.")

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