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

Sun Mar 26 22:21:31 2006 UTC (7 years, 1 month ago) by jj
File size: 1472 byte(s)
Initial import


    1 ##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
10 "PG.pl",
11 "PGbasicmacros.pl",
12 "PGchoicemacros.pl",
14 "PGauxiliaryFunctions.pl",
15 "PGgraphmacros.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.