FunctionDecomposition1

Function Decomposition

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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

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "answerComposition.pl", "AnswerFormatHelp.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:
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) \} \{ AnswerFormatHelp("formulas") \} $BR \( g(x) \) = \{ ans_rule(20) \} \{ AnswerFormatHelp("formulas") \} END_TEXT Context()->normalStrings;	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.html for more options and details.
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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