Composing Functions

Shows how to check that the answer is the composition of two functions.

Return to the PG docs home

Complete Code

Download file: ComposingFunctions.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'answerComposition.pl', 'PGcourse.pl');

Preamble

Include the macro answerComposition.pl.

Context()->variables->are(x => 'Real', y => 'Real', u => 'Real');

$a = random(2, 9);

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

Setup

This perl code sets up the problem. 
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) =`] [___]
END_PGML

Statement

This is the problem statement in PGML. 
COMPOSITION_ANS($f, $g);

Answer

Call the COMPOSITION_ANS method with the arguments $f and $g to test that the composition of the student answers for f and g is equal to the composition of the correct answers. Note that the COMPOSITION_ANS checker takes care to not allow certain trivial answers like f(u) = u and g(x) = sqrt(x^2 + $a).

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.