FunctionDecomposition1: Difference between revisions

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This article has been retained as a historical document.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This problem has been replaced with a newer version of this problem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

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

File location in OPL: FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1.pg
PGML location in OPL: FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1_PGML.pg

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

@@ Line 1: / Line 1: @@
+{{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has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/FunctionDecomposition.html a newer version of this problem]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>
-<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
+[[File:FunctionDecomposition1.png|300px|thumb|right|Click to enlarge]]
+<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.
-<ul>
-<li>Download file: [[File:FunctionDecomposition1.txt]] (change the file extension from txt to pg when you save it)</li>
-<li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/Precalc/FunctionDecomposition1.pg</code></li>
-</ul>
 </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]
+* 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]
+<br clear="all" />
 <p style="text-align:center;">
 [[SubjectAreaTemplates|Templates by Subject Area]]
@@ Line 16: / Line 22: @@
 <tr valign="top">
-<th> PG problem file </th>
+<th style="width: 50%"> PG problem file </th>
 <th> Explanation </th>
 </tr>
@@ Line 43: / Line 49: @@
 loadMacros(
-"PGstandard.pl",
+  'PGstandard.pl',
-"MathObjects.pl",
+  'MathObjects.pl',
-"answerComposition.pl",
+  'answerComposition.pl',
-"AnswerFormatHelp.pl",
+  'PGML.pl',
+  'PGcourse.pl'
 );
 TEXT(beginproblem());
 </pre>
@@ Line 87: / Line 93: @@
 <td style="background-color:#ffdddd;border:black 1px dashed;">
 <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>
 <td style="background-color:#ffcccc;padding:7px;">
@@ Line 121: / Line 124: @@
 <p>
 <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>
 </td>
@@ Line 131: / Line 134: @@
 <td style="background-color:#ddddff;border:black 1px dashed;">
 <pre>
-Context()->texStrings;
+BEGIN_PGML_SOLUTION
-BEGIN_SOLUTION
-${PAR}SOLUTION:${PAR}
 Solution explanation goes here.
-END_SOLUTION
+END_PGML_SOLUTION
-Context()->normalStrings;
-COMMENT('MathObject version.');
 ENDDOCUMENT();
@@ Line 155: / Line 153: @@
 [[Category:Top]]
-[[Category:Authors]]
+[[Category:Sample Problems]]
+[[Category:Subject Area Templates]]

FunctionDecomposition1: Difference between revisions

Latest revision as of 10:04, 18 July 2023

Function Decomposition

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