FunctionDecomposition1
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Function Decomposition
This PG code shows how to check student answers that are a composition of functions.
- Download file: File:FunctionDecomposition1.txt (change the file extension from txt to pg)
- File location in NPL:
NationalProblemLibrary/FortLewis/Authoring/Templates/Precalc
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "answerComposition.pl", "AnswerFormatHelp.pl", ); TEXT(beginproblem()); |
Initialization: |
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: |
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: |
Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;
COMMENT('MathObject version.');
ENDDOCUMENT();
|
Solution: |
