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# View of /trunk/NationalProblemLibrary/ASU-topics/setAlgebraFunctions/beth3algfun.pg

Sat Jun 3 14:35:45 2006 UTC (6 years, 11 months ago) by gage
File size: 1441 byte(s)
``` Cleaned code with convert-functions.pl script
```

```    1 ## DESCRIPTION
2 ## Algebra and Number Theory: Algebra
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('algebra', 'number', 'theory')
6 ## Tagged by YJ
7
8 ## Date('5/26/2005')
9 ## Author('Jeff Holt')
10 ## Institution('UVA')
11 ## TitleText1('Calculus')
12 ## EditionText1('5e')
13 ## AuthorText1('Stewart')
14 ## Section1('3.1.2')
15 ## Problem1(' ')
16
17 DOCUMENT();        # This should be the first executable line in the problem.
18
20 "PG.pl",
21 "PGbasicmacros.pl",
22 "PGchoicemacros.pl",
24 "PGauxiliaryFunctions.pl"
25 );
26
27 TEXT(beginproblem());
29
30 \$a = random(2,9,1);
31 \$b = non_zero_random(-9,9,1);
32 do {\$c = random(2,9,1)} until (\$c!=\$a);
33 \$d = non_zero_random(-9,9,1);
34
35 TEXT(EV2(<<EOT));
36
37 \$BR
38 Given that \(f(x)=\$a x ? {\$b}\) and \(g(x)=\$c x ? {\$d}\), calculate
39 \$BR
40 (a) \(f\circ g(x)\)= \{ans_rule(15)\}
41
42 \$BR
43 (b) \(g\circ f(x)\)= \{ans_rule(15)\}
44
45 \$BR
46 (c) \(f\circ f(x)\)= \{ans_rule(15)\}
47
48 \$BR
49 (d) \(g\circ g(x)\)= \{ans_rule(15)\}
50
51 \$BR
52 \$BR
53 EOT
54
55 \$ans1 = "\$a*(\$c*x + \$d)+\$b";
56 \$ans2 = "-infinity";
57 \$ans3 = "infinity";
58 \$ans4 = "\$c*(\$a*x + \$b)+\$d";
59 \$ans5 = "-infinity";
60 \$ans6 = "infinity";
61 \$ans7 = "\$a*(\$a*x + \$b)+\$b";
62 \$ans8 = "-infinity";
63 \$ans9 = "infinity";
64 \$ans10 = "\$c*(\$c*x + \$d)+\$d";
65 \$ans11 = '-infinity';
66 \$ans12 = 'infinity';
67 ANS(fun_cmp(\$ans1));
68
69 ANS(fun_cmp(\$ans4));
70
71 ANS(fun_cmp(\$ans7));
72
73 ANS(fun_cmp(\$ans10));
74
75
76 ENDDOCUMENT();        # This should be the last executable line in the problem.
77
```