ComposingFunctions

This article has been retained as a historical document.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This problem has been replaced with a newer version of this problem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

• POD documentation: answerComposition.pl
• PG macro: answerComposition.pl