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

Sun Oct 25 03:55:33 2009 UTC (3 years, 7 months ago) by jj
File size: 1868 byte(s)
```Fixed bug 1694, intervals in answer should be half closed.
```

```    1 ## DESCRIPTION
2 ## Algebra
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('function' 'graph' 'slope')
6 ## Tagged by tda2d
7
8 ## 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 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGgraphmacros.pl",
30 "PGasu.pl",
31 );
32
33 TEXT(beginproblem());
35
36 \$a = random(1,5,1);
37 \$b = random(-5,0,1);
38
39 \$graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]);
40 \$f = FEQ("abs(x-\$a)+abs(x+\$a)+\$b for x in <-10,10> using color:green and weight:2");
41
42 plot_functions(\$graph,\$f);
43
44 BEGIN_TEXT
45 \$BR
46
47 Consider the function whose graph is sketched:
48 \$BR \{ image(insertGraph(\$graph), width=>200, height=>200) \} \$BR
49 Find the intervals over which the function is strictly increasing or
50 strictly decreasing.
52 \$BR \$BR
53 The interval over which the function is strictly increasing: \{ans_rule(35) \}
54 \$BR
55 The interval over which the function is strictly decreasing: \{ans_rule(35) \}
56 END_TEXT
57
58 #ANS(interval_cmp("[\$a,infty)", sloppy=>"yes"));
59 ANS(pc_evaluator([ [interval_cmp("[\$a,infty)"),1],
60 [interval_cmp("[\$a,infty)", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
61 ANS(pc_evaluator([ [interval_cmp("(-infinity, -\$a]"),1],
62 [interval_cmp("(-infinity, -\$a]", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
63
64
65
66 ENDDOCUMENT();        # This should be the last executable line in the problem.
```