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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra16FunctionGraphs/lh2-3_30a.pg

Revision 1148 - (download) (annotate)
Tue Oct 27 02:32:29 2009 UTC (3 years, 6 months ago) by jj
File size: 1876 byte(s)
```Fixed bug 1695, answer should be half closed intervals.
```

```    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
22 loadMacros(
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
26 "PGanswermacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGgraphmacros.pl",
29 "extraAnswerEvaluators.pl",
30 "PGasu.pl"
31 );
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 \$graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]);
44 \$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 Find the intervals over which the function is strictly increasing or
54 decreasing.  Express your answer in \{ helpLink('interval notation')\}.
55 \$BR \$BR
56 The interval over which the function is strictly increasing: \{ans_rule(35) \}
57 \$BR
58 The interval over which the function is strictly decreasing: \{ans_rule(35) \}
59 \$PAR
60 END_TEXT
61
62 \$h1=-\$h;
63
64 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
69 ENDDOCUMENT();        # This should be the last executable line in the problem.
```

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