FunctionDecomposition1: Difference between revisions

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{{historical}}
<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has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/FunctionDecomposition.html a newer version of this problem]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>
<h2>Function Decomposition</h2>
<h2>Function Decomposition</h2>


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</p>
</p>
* 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]
* 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]
* 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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<tr valign="top">
<tr valign="top">
<th> PG problem file </th>
<th style="width: 50%"> PG problem file </th>
<th> Explanation </th>
<th> Explanation </th>
</tr>
</tr>
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loadMacros(
loadMacros(
"PGstandard.pl",
  'PGstandard.pl',
"MathObjects.pl",
  'MathObjects.pl',
"answerComposition.pl",
  'answerComposition.pl',
"AnswerFormatHelp.pl",
  'PGML.pl',
  'PGcourse.pl'
);
);
TEXT(beginproblem());
TEXT(beginproblem());
</pre>
</pre>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
<td style="background-color:#ffdddd;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML
BEGIN_TEXT
Express the function [` y = \sqrt{ x^2 + [$a] } `]
Express the function \( y = \sqrt{ x^2 + $a } \)
as a composition [` y = f(g(x)) `] of two simpler
as a composition \( y = f(g(x)) \) of two simpler
functions [` y = f(u) `] and [` u = g(x) `].
functions \( y = f(u) \) and \( u = g(x) \).
 
$BR
+ [` f(u) = `] [_______________]
$BR
 
\( f(u) \) = \{ ans_rule(20) \}
+ [` g(x) = `]  [_______________]
\{ AnswerFormatHelp("formulas") \}
 
$BR
[@ helpLink('formula') @]*
\( g(x) \) = \{ ans_rule(20) \}
END_PGML
\{ AnswerFormatHelp("formulas") \}
END_TEXT
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>
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.
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>
Context()->texStrings;
BEGIN_PGML_SOLUTION
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
Solution explanation goes here.
END_SOLUTION
END_PGML_SOLUTION
Context()->normalStrings;
 
COMMENT('MathObject version.');


ENDDOCUMENT();
ENDDOCUMENT();

Latest revision as of 10:04, 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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