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| 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. |
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