Difference between revisions of "FunctionDecomposition1"
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(Created page with '<h2>Function Decomposition</h2> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> This PG code shows how to check student answers that are a composition o…') |
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<b>Initialization:</b> |
<b>Initialization:</b> |
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| + | We need to include the macros file <code>answerComposition.pl</code>, which provides an answer checker that determines if two functions compose to form a given function. This can be used in problems where you ask a student to break a given function into a composition of two simpler functions, neither of which is allowed to be the identity function. |
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<b>Answer Evaluation:</b> |
<b>Answer Evaluation:</b> |
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| + | We use the <code>COMPOSITION_ANS()</code> routine to evaluate both answer blanks. It is possible to use the same variable for both answer blanks. See [http://webwork.maa.org/pod/pg_TRUNK/macros/answerComposition.pl.html answerComposition.pl.html] for more options and details. |
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Revision as of 00:40, 1 December 2010
Function Decomposition
This PG code shows how to check student answers that are a composition of functions.
- Download file: File:FunctionDecomposition1.txt (change the file extension from txt to pg)
- File location in NPL:
NationalProblemLibrary/FortLewis/Authoring/Templates/Precalc
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "answerComposition.pl", "AnswerFormatHelp.pl", ); TEXT(beginproblem()); |
Initialization:
We need to include the macros file |
Context("Numeric");
Context()->variables->are(x=>"Real",y=>"Real",u=>"Real");
$a = random(2,9,1);
$f = Formula("sqrt(u)");
$g = Formula("x^2+$a");
|
Setup: |
Context()->texStrings;
BEGIN_TEXT
Express the function \( y = \sqrt{ x^2 + $a } \)
as a composition \( y = f(g(x)) \) of two simpler
functions \( y = f(u) \) and \( u = g(x) \).
$BR
$BR
\( f(u) \) = \{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$BR
\( g(x) \) = \{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
END_TEXT
Context()->normalStrings;
|
Main Text: |
$showPartialCorrectAnswers = 1; COMPOSITION_ANS( $f, $g, vars=>['u','x'], showVariableHints=>1); |
Answer Evaluation:
We use the |
Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;
COMMENT('MathObject version.');
ENDDOCUMENT();
|
Solution: |
