FunctionDecomposition1

Function Decomposition

Click to enlarge

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