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…')
 
(add historical tag and give links to newer problems.)
 
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{{historical}}
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<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/FunctionDecomposition.html a newer version of this problem]</p>
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<h2>Function Decomposition</h2>
  
<h2>Function Decomposition</h2>
   
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<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
  
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[[File:FunctionDecomposition1.png|300px|thumb|right|Click to enlarge]]
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<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
 
This PG code shows how to check student answers that are a composition of functions.
  
This PG code shows how to check student answers that are a composition of functions.
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<ul>
  
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<li>Download file: [[File:FunctionDecomposition1.txt]] (change the file extension from txt to pg)</li>
  
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<li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/Precalc</code></li>
  
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</ul>
  
 
</p>
  
</p>
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* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1.pg FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1.pg]
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* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1_PGML.pg FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1_PGML.pg]
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<br clear="all" />
 
<p style="text-align:center;">
  
<p style="text-align:center;">
 
[[SubjectAreaTemplates|Templates by Subject Area]]
  
[[SubjectAreaTemplates|Templates by Subject Area]]
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<tr valign="top">
  
<tr valign="top">
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<th> PG problem file </th>
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<th style="width: 50%"> PG problem file </th>
 
<th> Explanation </th>
  
<th> Explanation </th>
 
</tr>
  
</tr>
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loadMacros(
  
loadMacros(
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"PGstandard.pl",
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'PGstandard.pl',
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"MathObjects.pl",
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'MathObjects.pl',
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"answerComposition.pl",
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'answerComposition.pl',
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"AnswerFormatHelp.pl",
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'PGML.pl',
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'PGcourse.pl'
 
);
  
);
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TEXT(beginproblem());
  
TEXT(beginproblem());
 
</pre>
  
</pre>
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<p>
  
<p>
 
<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.
 
</p>
  
</p>
 
</td>
  
</td>
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<pre>
  
<pre>
 
Context("Numeric");
  
Context("Numeric");
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Context()->variables->are(x=>"Real",y=>"Real",u=>"Real");
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Context()->variables->add(u=>"Real");
   
 
$a = random(2,9,1);
  
$a = random(2,9,1);
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<td style="background-color:#ffdddd;border:black 1px dashed;">
  
<td style="background-color:#ffdddd;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
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BEGIN_PGML
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BEGIN_TEXT
  
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Express the function [` y = \sqrt{ x^2 + [$a] } `]
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Express the function \( y = \sqrt{ x^2 + $a } \)
 
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as a composition [` y = f(g(x)) `] of two simpler
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as a composition \( y = f(g(x)) \) of two simpler
  
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functions [` y = f(u) `] and [` u = g(x) `].
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functions \( y = f(u) \) and \( u = g(x) \).
  
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−
$BR
  
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+ [` f(u) = `] [_______________]
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$BR
  
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\( f(u) \) = \{ ans_rule(20) \}
  
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+ [` g(x) = `] [_______________]
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\{ AnswerFormatHelp("formulas") \}
  
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$BR
  
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[@ helpLink('formula') @]*
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\( g(x) \) = \{ ans_rule(20) \}
  
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END_PGML
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\{ AnswerFormatHelp("formulas") \}
  
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END_TEXT
  
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Context()->normalStrings;
  
 
</pre>
  
</pre>
 
<td style="background-color:#ffcccc;padding:7px;">
  
<td style="background-color:#ffcccc;padding:7px;">
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<p>
  
<p>
 
<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/macros/answerComposition.html answerComposition.pl] for more options and details.
 
</p>
  
</p>
 
</td>
  
</td>
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<td style="background-color:#ddddff;border:black 1px dashed;">
  
<td style="background-color:#ddddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
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BEGIN_PGML_SOLUTION
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BEGIN_SOLUTION
  
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${PAR}SOLUTION:${PAR}
  
 
Solution explanation goes here.
  
Solution explanation goes here.
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END_SOLUTION
  
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END_PGML_SOLUTION
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Context()->normalStrings;
  
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COMMENT('MathObject version.');
  
   
 
ENDDOCUMENT();
  
ENDDOCUMENT();
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[[Category:Top]]
  
[[Category:Top]]
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[[Category:Authors]]
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[[Category:Sample Problems]]
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[[Category:Subject Area Templates]]

Latest revision as of 05:04, 18 July 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem


Function Decomposition

Click to enlarge

This PG code shows how to check student answers that are a composition of functions.



Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros(
  'PGstandard.pl',
  'MathObjects.pl',
  'answerComposition.pl',
  'PGML.pl',
  'PGcourse.pl'
);
TEXT(beginproblem());

Initialization: We need to include the macros file answerComposition.pl, 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. 

Context("Numeric");
Context()->variables->add(u=>"Real");

$a = random(2,9,1);

$f = Formula("sqrt(u)");
$g = Formula("x^2+$a");

Setup: 

BEGIN_PGML
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) `].

+ [` f(u) = `] [_______________]

+ [` g(x) = `]  [_______________]

[@ helpLink('formula') @]*
END_PGML

Main Text: 

$showPartialCorrectAnswers = 1;

COMPOSITION_ANS( $f, $g, vars=>['u','x'], showVariableHints=>1);

Answer Evaluation: We use the COMPOSITION_ANS() routine to evaluate both answer blanks. It is possible to use the same variable for both answer blanks. See answerComposition.pl for more options and details. 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution:

Templates by Subject Area

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