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| 1 : | jjholt | 156 | ## DESCRIPTION |
| 2 : | ## Algebra | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 145 | |
| 5 : | jjholt | 156 | ## KEYWORDS('function' 'graph' 'slope') |
| 6 : | ## Tagged by tda2d | ||
| 7 : | jj | 145 | |
| 8 : | jjholt | 156 | ## 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 : | jj | 145 | 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 : | jj | 1148 | "extraAnswerEvaluators.pl", |
| 30 : | "PGasu.pl" | ||
| 31 : | jj | 145 | ); |
| 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 : | jj | 1148 | $graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]); |
| 44 : | jj | 145 | $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 : | jj | 1148 | Find the intervals over which the function is strictly increasing or |
| 54 : | decreasing. Express your answer in \{ helpLink('interval notation')\}. | ||
| 55 : | jj | 145 | $BR $BR |
| 56 : | jj | 1148 | The interval over which the function is strictly increasing: \{ans_rule(35) \} |
| 57 : | jj | 145 | $BR |
| 58 : | jj | 1148 | The interval over which the function is strictly decreasing: \{ans_rule(35) \} |
| 59 : | jj | 145 | $PAR |
| 60 : | END_TEXT | ||
| 61 : | |||
| 62 : | $h1=-$h; | ||
| 63 : | |||
| 64 : | jj | 1148 | 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 : | jj | 145 | |
| 69 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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