## DESCRIPTION ## Algebra ## ENDDESCRIPTION ## KEYWORDS('function' 'graph' 'slope') ## Tagged by tda2d ## DBsubject('Algebra') ## DBchapter('Functions') ## DBsection('Average Rate of Change: Increasing and Decreasing Functions') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGgraphmacros.pl", "extraAnswerEvaluators.pl", "PGasu.pl" ); TEXT(beginproblem()); \$showPartialCorrectAnswers = 1; \$h = non_zero_random(-5,5,1); \$k = random(-6,1,1); # f(x)=(x+h)^2+k \$b = \$h*2; \$c = (\$h)**2+\$k; \$graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]); \$f = FEQ("x**2 + \$b x +\$c for x in <-10,10> using color:green and weight:2"); plot_functions(\$graph,\$f); BEGIN_TEXT \$BR Consider the function whose graph is sketched: \$BR \{ image(insertGraph(\$graph), width=>200, height=>200) \} \$BR Find the intervals over which the function is strictly increasing or decreasing. Express your answer in \{ helpLink('interval notation')\}. \$BR \$BR The interval over which the function is strictly increasing: \{ans_rule(35) \} \$BR The interval over which the function is strictly decreasing: \{ans_rule(35) \} \$PAR END_TEXT \$h1=-\$h; ANS(pc_evaluator([ [interval_cmp("[\$h1,infty)"),1], [interval_cmp("[\$h1,infty)", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']])); ANS(pc_evaluator([ [interval_cmp("(-infinity, \$h1]"),1], [interval_cmp("(-infinity, \$h1]", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']])); ENDDOCUMENT(); # This should be the last executable line in the problem.