View of /trunk/NationalProblemLibrary/Rochester/setAlgebra16FunctionGraphs/lh2-3_48a.pg

    1 ##DESCRIPTION
    2 ##  lh2-3_48a.pg.
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'increasing and decreasing functions')
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl",
   15 "PGgraphmacros.pl",
   16 "extraAnswerEvaluators.pl"
   17 
   18 );
   19 
   20 TEXT(beginproblem());
   21 $showPartialCorrectAnswers = 1;
   22 
   23 $a = random(1,5,1);
   24 $b = random(-5,0,1);
   25 
   26 $graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[200,200]);
   27 $f = FEQ("abs(x-$a)+abs(x+$a)+$b for x in <-10,10> using color:green and weight:2");
   28 
   29 plot_functions($graph,$f);
   30 
   31 BEGIN_TEXT
   32 $BR
   33 
   34 Consider the function whose graph is sketched:
   35 $BR \{ image(insertGraph($graph), width=>200, height=>200) \} $BR
   36 Find the intervals over which the function is increasing or decreasing. If the answer includes more than one interval write the intervals separated by
   37 the "union" symbol, U. You may use "infinity" for \(\infty\) and "-infinity" for \(-\infty\). For example, you may write (-infinity, 5] for the interval \((-\infty,5]\) and (-infinity, 5]U(7,9) for \((-\infty,5]\cup (7,9)\).
   38 $BR $BR
   39 The interval over which the function is increasing: \{ans_rule(35) \}
   40 $BR
   41 The interval over which the function is decreasing: \{ans_rule(35) \}
   42 $PAR
   43 END_TEXT
   44 
   45 ANS(interval_cmp("($a,infty)"));
   46 ANS(interval_cmp("(-infty,-$a)"));
   47 
   48 
   49 
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.