Difference between revisions of "ComposingFunctions"

From WeBWorK_wiki
Jump to navigation Jump to search
 
(3 intermediate revisions by 3 users not shown)
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been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/problem-techniques/ComposingFunctions.html a newer version of this problem]</p>
 
<h2>Composing Functions</h2>
  
<h2>Composing Functions</h2>
   
Line 104: Line 107:
 
<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/doc/cvs/pg_CURRENT/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>
Line 120: Line 123:
   
 
<ul>
  
<ul>
−
<li>POD documentation: [http://webwork.maa.org/doc/cvs/pg_CURRENT/macros/answerComposition.pl.html answerComposition.pl.html]</li>
 +
<li>POD documentation: [http://webwork.maa.org/pod/pg/macros/answerComposition.html answerComposition.pl]</li>
−
<li>PG macro: [http://cvs.webwork.rochester.edu/viewcvs.cgi/pg/macros/answerComposition.pl answerComposition.pl]</li>
 +
<li>PG macro: [http://webwork.maa.org/viewvc/system/trunk/pg/macros/answerComposition.pl?view=log answerComposition.pl]</li>
 
</ul>
  
</ul>

Latest revision as of 08:11, 28 June 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This article has been retained as a historical document.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This problem has been replaced with a newer version of this problem

Composing Functions


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

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"answerComposition.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->are(x=>"Real",y=>"Real",u=>"Real");

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

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

Setup: Everything is as usual. 

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) \}
$BR
\( g(x) \) = \{ ans_rule(20) \}
END_TEXT
Context()->normalStrings;

Main Text: The text section is as we'd expect. 

$showPartialCorrectAnswers = 1;

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

ENDDOCUMENT();

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.

Problem Techniques Index



Retrieved from "https://webwork.maa.org/mediawiki_new/index.php?title=ComposingFunctions&oldid=23651"