FunctionDecomposition1

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Function Decomposition

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



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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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