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Finite Mathematics Applied to the Real World	Calculus Applied to the Real World	Finite Mathematics & Calculus Applied to the Real World

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.")

13. g(x) = (x 1)2	Answer for 13	14. h(x) = (2x)2
15. s(x) = x 2 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	20. s(x) = x2 3
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.

31. Answer	32.	33. Answer
34.	35. Answer	36.
37. Answer	38.	39. Answer

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

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Finite Mathematics Applied to the Real World	Calculus Applied to the Real World	Finite Mathematics & Calculus Applied to the Real World