ComposingFunctions
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Composing Functions
This PG code shows how to check student answers that are a composition of functions.
PG problem file | Explanation |
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DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "answerComposition.pl", "PGcourse.pl", ); TEXT(beginproblem()); |
Initialization:
We need to include the macros file |
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 |
- POD documentation: answerComposition.pl
- PG macro: answerComposition.pl