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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra16FunctionGraphs/c0s5p4.pg

Sun Mar 26 22:21:31 2006 UTC (7 years, 1 month ago) by jj
File size: 2111 byte(s)
Initial import


    1 #DESCRIPTION
2 #KEYWORDS('functions', 'domain', 'graph', 'maximum/minimum')
3 # Identify existence of a max or min for a function on various intervals -- use calculator to find the graph.
4 # Warm up for theorem about existence of extrema.
5 #ENDDESCRIPTION
6
7 DOCUMENT();        # This should be the first executable line in the problem.
8
10            "PGbasicmacros.pl",
11            "PGchoicemacros.pl",
13 "PGauxiliaryFunctions.pl");
14
15 TEXT(beginproblem());
16 $showPartialCorrectAnswers = 0; 17 18 BEGIN_TEXT 19 Determine which of the following statements are true and which are false. 20 Enter the T or F in front of each statement. 21$BR
22  Remember that $$x\in(-1,1)$$ is the same as
23  $$-1 LTS x LTS 1$$ $BR 24 and $$x\in[-1,1]$$ means $$-1 LTE x LTE 1$$. 25$PAR
26 END_TEXT
27 @questStr = ();
28 @ansStr = ();
29 qa( ~~@questStr, ~~@ansStr,
30 EV2("The function $$f(x)=x^3$$ with domain $$x\in(-3,3)$$ has at
31 least one input which produces a largest output value."),
32    "F",
33 "The function $$f(x)=x^3$$ with domain $$x\in(-3,3)$$ has at least one input which produces a smallest output value.",
34    "F",
35 "The function $$f(x)=x^3$$ with domain $$x\in[-3,3]$$ has at least one input which produces a largest output value.",
36    "T",
37 "The function $$f(x)=x^3$$ with domain $$x\in[-3,3]$$ has at least one input which produces a smallest output value.",
38    "T",
39 "The function $$\sin(x)$$ on the domain $$x\in(-\pi,\pi)$$ has at least one input which produces a largest output value.",
40    "T",
41 "The function $$\sin(x)$$ on the domain $$x\in(-\pi,\pi)$$ has at least one input which produces a smallest output value.",
42    "T",
43 "The function $$\sin(x)$$ on the domain $$x\in[-\pi,\pi]$$ has at least one input which produces a largest output value.",
44    "T",
45 "The function $$\sin(x)$$ on the domain $$x\in[-\pi,\pi]$$ has at least one input which produces a smallest output value.",
46    "T",
47   );
48 @slice = NchooseK(8,5);
49 BEGIN_TEXT
50 \{match_questions_list(@questStr[@slice])\}
51 END_TEXT
52 @ans =  @ansStr[@slice];
53 ANS(str_cmp([ @ans ]   )   );
54 ENDDOCUMENT();        # This should be the last executable line in the problem.