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C-18 Appendix C MINI PROJECT Correcting a Graphing Utility Display As background for this discussion, you need to recall the definitions from intermediate algebra for expressions of the form 1 n x and x 1n , where n is a positive integer. See Appendices B.2 and B.3 if you need a reminder, or have someone in the group consult the appendix and present the definitions and relevant examples to the group at large. Some graphing utilities produce incomplete graphs for root functions y 1 n x when n is an odd integer. To find out how your graphing utility operates in this respect, try the function y 1 3 x on your graphing utility, and compare your result to Figures A and B. (You might need to enter the function in the form y x 13 .) The reason for the incomplete graph in Figure A is that the graphing utility used requires nonnegative inputs in computing roots, even cube roots. Suppose for this discussion that you have this type of graphing utility. Find a way to use the techniques in this section to produce a correct graph, one similar to that shown in Figure B. 2 2 0 0 _2 _3 0 3 Figure A An incomplete graph of y 1 3 x _2 _3 0 3 Figure B A complete graph of y 1 3 x
Appendix C C-19 MINI PROJECT A Graphical Approach to Composition of Functions As we saw in this section, the iteration process can be carried out either algebraically or graphically. Composition of functions can also be represented graphically. The accompanying figure shows the graphs of two functions f and g, the line y x, and an input a. Use the figure and the ideas of this section to discover the coordinates of the four indicated points. In particular, explain how to find the point (a, g[ f(a)]) on the graph of the composite function g f. y y=x y=g(x) y=ƒ a x
Page 1 and 2: APPENDIX C Title and Page Number Pr
Page 3 and 4: Appendix C C-3 MINI PROJECT Discuss
Page 5 and 6: Appendix C C-5 MINI PROJECT Thinkin
Page 7 and 8: Appendix C C-7 1. equilateral trian
Page 9 and 10: Appendix C C-9 MINI PROJECT Flying
Page 11 and 12: Appendix C C-11 MINI PROJECT An Ine
Page 13 and 14: Appendix C C-13 (a) The two data po
Page 15 and 16: Appendix C C-15 and http://www.svob
Page 17: Appendix C C-17 For Figure D we can
Page 21 and 22: Appendix C C-21 MINI PROJECT Who Ar
Page 23 and 24: Appendix C C-23 MINI PROJECT 1 How
Page 25 and 26: Appendix C C-25 either the quadrati
Page 27 and 28: Appendix C C-27 PROJECT The Least-S
Page 29 and 30: Appendix C C-29 Then, for any line
Page 31 and 32: Appendix C C-31 PROJECT Finding Som
Page 33 and 34: Appendix C C-33 3. When a person co
Page 35 and 36: Appendix C C-35 2. Use part (b) of
Page 37 and 38: Appendix C C-37 PROJECT Coffee Temp
Page 39 and 40: Appendix C C-39 MINI PROJECT More C
Page 41 and 42: Appendix C C-41 The calculations co
Page 43 and 44: Appendix C C-43 PROJECT Transits of
Page 45 and 46: Appendix C C-45 E A ¨ V ¨ Bª d S
Page 47 and 48: Appendix C C-47 PROJECT A Linear Ap
Page 49 and 50: Appendix C C-49 Continuing with the
Page 51 and 52: Appendix C C-51 PROJECT Constructin
Page 53 and 54: Appendix C C-53 1 y Figure A A grap
Page 55 and 56: Appendix C C-55 PROJECT Fourier Ser
Page 57 and 58: Appendix C C-57 sine and cosine fun
Page 59 and 60: Appendix C C-59 PROJECT The Motion
Page 61 and 62: Appendix C C-61 PROJECT The Design
Page 63 and 64: Appendix C C-63 denote the angles o
Page 65 and 66: Appendix C C-65 inverse trigonometr
Page 67 and 68: Appendix C C-67 PROJECT Inverse Sec
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Appendix C C-69 Alternatively, usin
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Appendix C C-71 PROJECT Snell’s L
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Appendix C C-73 vertically downward
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0 0 0 Appendix C C-75 PROJECT Vecto
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Appendix C C-77 Exercise 8 We outli
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Appendix C C-79 y y=2x+5 Îy=2 A (1
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 Appendi
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Appendix C C-83 PROJECT Parameteriz
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Appendix C C-85 It is worth noting
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Appendix C C-87 6. Show that the li
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Appendix C C-89 2. An altitude of a
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Appendix C C-91 PROJECT The Leontie
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Appendix C C-93 n x units of that
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Appendix C C-95 him/herself through
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Appendix C C-97 PROJECT The Leontie
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Appendix C C-99 As in the solution
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Appendix C C-101 MINI PROJECT 2 Con
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Appendix C C-103 PROJECT Using Hype
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Appendix C C-105 PROJECT Two Method
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Appendix C C-107 (b) Use Method 1 t
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Appendix C C-109 MINI PROJECT An Un
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Appendix C C-111 PROJECT More on Su
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Appendix C C-113 SOLUTION 25 25 a (
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Appendix C C-115 4. Simplify the fo
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