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| 1 : | gage | 731 | ##DESCRIPTION |
| 2 : | ## Introduction to Functions | ||
| 3 : | ## | ||
| 4 : | ##ENDDESCRIPTION | ||
| 5 : | ## DBsubject('Intermediate Algebra') | ||
| 6 : | ## DBchapter('Ch 02: Functions and Linear Functions') | ||
| 7 : | ## DBsection('Introduction to Functions') | ||
| 8 : | ## KEYWORDS('functions') | ||
| 9 : | ## TitleText1('Essentials of Intermediate Algebra') | ||
| 10 : | ## EditionText1('1') | ||
| 11 : | ## AuthorText1('Blitzer') | ||
| 12 : | ## Section1('2.1') | ||
| 13 : | ## Problem1('') | ||
| 14 : | ## Author('RA Cruz') | ||
| 15 : | ## Institution('The College of Idaho') | ||
| 16 : | ## Date: 2007/09 | ||
| 17 : | |||
| 18 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 19 : | |||
| 20 : | loadMacros( | ||
| 21 : | "PGstandard.pl", | ||
| 22 : | "MathObjects.pl", | ||
| 23 : | "contextLimitedNumeric.pl", | ||
| 24 : | "contextPiecewiseFunction.pl" | ||
| 25 : | ); | ||
| 26 : | |||
| 27 : | TEXT(beginproblem); | ||
| 28 : | |||
| 29 : | ###################################### | ||
| 30 : | # Setup | ||
| 31 : | |||
| 32 : | Context("PiecewiseFunction"); | ||
| 33 : | |||
| 34 : | $m1 = random(2,5,1); | ||
| 35 : | $b1 = random(1,6,1); | ||
| 36 : | $m2 = random(2,5,1); | ||
| 37 : | $b2 = random(1,6,1); | ||
| 38 : | $x = random(-4,4,1); | ||
| 39 : | |||
| 40 : | $h = Formula("$m1 x + $b1 if x < $x else $m2 x - $b2 if x >= $x"); | ||
| 41 : | |||
| 42 : | @xnum = (random($x-5,$x-1,1),random($x+1,$x1+5,1),$x); | ||
| 43 : | @slice = NchooseK(3,3); | ||
| 44 : | @input = @xnum[@slice]; | ||
| 45 : | |||
| 46 : | ###################################### | ||
| 47 : | # Main text | ||
| 48 : | |||
| 49 : | BEGIN_TEXT | ||
| 50 : | The following function is defined by two equations. The equation in the | ||
| 51 : | first row gives the output for values of \(x\) less than | ||
| 52 : | $x. The equation in the second row gives the ouput for values | ||
| 53 : | of \(x\) which are greater or equal to $x. | ||
| 54 : | |||
| 55 : | \[ h(x) = \{$h->TeX\} \] | ||
| 56 : | |||
| 57 : | Find the indicated values: | ||
| 58 : | $PAR | ||
| 59 : | a) \( h($input[0]) \) = \{ans_rule(15)\} | ||
| 60 : | $PAR | ||
| 61 : | b) \( h($input[1]) \) = \{ans_rule(15)\} | ||
| 62 : | $PAR | ||
| 63 : | c) \( h($input[2]) \) = \{ans_rule(15)\} | ||
| 64 : | END_TEXT | ||
| 65 : | |||
| 66 : | ###################################### | ||
| 67 : | # Answers | ||
| 68 : | |||
| 69 : | Context("LimitedNumeric"); | ||
| 70 : | Context()->strings->add("No solution"=>{}, | ||
| 71 : | "Not defined"=>{}, | ||
| 72 : | "Does not exist"=> {}, | ||
| 73 : | "All real numbers"=>{}); | ||
| 74 : | |||
| 75 : | $ans_a = $h->eval(x=>$input[0])->inContext(Context()); | ||
| 76 : | ANS($ans_a->cmp); | ||
| 77 : | |||
| 78 : | $ans_b = $h->eval(x=>$input[1])->inContext(Context()); | ||
| 79 : | ANS($ans_b->cmp); | ||
| 80 : | |||
| 81 : | $ans_c = $h->eval(x=>$input[2])->inContext(Context()); | ||
| 82 : | ANS($ans_c->cmp); | ||
| 83 : | |||
| 84 : | $showPartialCorrectAnswers = 1; | ||
| 85 : | |||
| 86 : | ###################################### | ||
| 87 : | |||
| 88 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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