View of /trunk/NationalProblemLibrary/Rochester/setAlgebra16FunctionGraphs/lh2-3_30a.pg

    1 ## DESCRIPTION
    2 ## Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('function' 'graph' 'slope')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Functions')
   10 ## DBsection('Average Rate of Change: Increasing and Decreasing Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGgraphmacros.pl",
   29 "extraAnswerEvaluators.pl",
   30 "PGasu.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $h =  non_zero_random(-5,5,1);
   37 $k =  random(-6,1,1);
   38 
   39 # f(x)=(x+h)^2+k
   40 $b = $h*2;
   41 $c = ($h)**2+$k;
   42 
   43 $graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]);
   44 $f = FEQ("x**2 + $b x +$c for x in <-10,10> using color:green and weight:2");
   45 
   46 plot_functions($graph,$f);
   47 
   48 BEGIN_TEXT
   49 $BR
   50 
   51 Consider the function whose graph is sketched:
   52 $BR \{ image(insertGraph($graph), width=>200, height=>200) \} $BR
   53 Find the intervals over which the function is strictly increasing or
   54 decreasing.  Express your answer in \{ helpLink('interval notation')\}.
   55 $BR $BR
   56 The interval over which the function is strictly increasing: \{ans_rule(35) \}
   57 $BR
   58 The interval over which the function is strictly decreasing: \{ans_rule(35) \}
   59 $PAR
   60 END_TEXT
   61 
   62 $h1=-$h;
   63 
   64 ANS(pc_evaluator([ [interval_cmp("[$h1,infty)"),1],
   65 [interval_cmp("[$h1,infty)", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
   66 ANS(pc_evaluator([ [interval_cmp("(-infinity, $h1]"),1],
   67 [interval_cmp("(-infinity, $h1]", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
   68 
   69 ENDDOCUMENT();        # This should be the last executable line in the problem.