[rochester] / tags / rel-1-9-02 / rochester_problib / setAlgebra23PolynomialZeros / describe_graph_b.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /tags/rel-1-9-02/rochester_problib/setAlgebra23PolynomialZeros/describe_graph_b.pg

Wed Jul 30 22:57:48 2003 UTC (9 years, 9 months ago)
File size: 2164 byte(s)
`This commit was manufactured by cvs2svn to create tag 'rel-1-9-02'.`

```    1 ##DESCRIPTION
2 ##KEYWORDS('logarithms,exponentials','exponential growth,decay')
3 ##TYPE('word problem')
4 ##ENDDESCRIPTION
5
6 DOCUMENT();        # This should be the first executable line in the problem.
7
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.pl",
13 "PGauxiliaryFunctions.pl"
14 );
15
16 TEXT(&beginproblem);
18
19 \$A = non_zero_random(-9,9,1);
20 \$B = non_zero_random(-9,9,1);
21 while (\$A == \$B) { \$B = non_zero_random(-9,9,1);}
22 \$C = non_zero_random(-9,9,1);
23 while (\$A == \$C || \$B == \$C) {\$C = non_zero_random(-9,9,1);}
24
25 \$K = non_zero_random(-9,9,1);
26
27 \$E1 = random(2,9,1);
28 \$E2 = random(2,9,1);
29 \$E3 = random(2,9,1);
30
31 @root = num_sort((\$A,\$B,\$C));
32
33 \$funct = "\$K(x-\$root[0])^\$E1 (x-\$root[1])^\$E2 (x-\$root[2])^\$E3 ";
34
35 if (\$K*(-1)**\$E1 * (\$root[0]-1-\$root[2])**\$E2 * (\$root[0]-1-\$root[2])**\$E3 < 0){
36         \$region[0] = -1;}
37 else {\$region[0] = 1;}
38
39 if (int \$E1/2 == \$E1/2) {\$region[1] = \$region[0];}
40 else {\$region[1] = -\$region[0];}
41
42 if (int \$E2/2 == \$E2/2) {\$region[2] = \$region[1];}
43 else {\$region[2] = -\$region[1];}
44
45 if (int \$E3/2 == \$E3/2) {\$region[3] = \$region[2];}
46 else {\$region[3] = -\$region[2];}
47
48 foreach \$i (0..3) {
49         if (\$region[\$i] > 0) {\$ans[\$i] = "above";}
50         else {\$ans[\$i] = "below";}
51 }
52
53 BEGIN_TEXT;
54 Given \(f(x) = \$funct\), find the roots in increasing order.
55 \$BR
56 The roots are \{ans_rule(5)\}, \{ans_rule(5)\}, and \{ans_rule(5)\}.
57 \$BR
58 To the left of the first root, is the graph of \(f(x)\) above or below the
59 x-axis?  Answer above or below: \{ans_rule(5)\}.
60 \$BR
61 Between the first two roots, is the graph of \(f(x)\) above or below the
62 x-axis?  Answer above or below: \{ans_rule(5)\}.
63 \$BR
64 Between the last two roots, is the graph of \(f(x)\) above or below the
65 x-axis?  Answer above or below: \{ans_rule(5)\}.
66 \$BR
67 After the last root, is the graph of \(f(x)\) above or below the x-axis?
68 Answer above or below: \{ans_rule(5)\}
69 END_TEXT
70
71 &ANS(num_cmp(\$root[0]));
72 &ANS(num_cmp(\$root[1]));
73 &ANS(num_cmp(\$root[2]));
74 &ANS(str_cmp(\$ans[0]));
75 &ANS(str_cmp(\$ans[1]));
76 &ANS(str_cmp(\$ans[2]));
77 &ANS(str_cmp(\$ans[3]));
78
79 ENDDOCUMENT();        # This should be the last executable line in the problem.
80
```