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

 1 : jj 145 ##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.