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

    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 
    9 loadMacros("PG.pl",
   10            "PGbasicmacros.pl",
   11            "PGchoicemacros.pl",
   12            "PGanswermacros.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.