Difference between revisions of "FunctionDecomposition1"
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<tr valign="top"> |
<tr valign="top"> |
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| − | <th> PG problem file </th> |
+ | <th style="width: 40%"> PG problem file </th> |
<th> Explanation </th> |
<th> Explanation </th> |
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</tr> |
</tr> |
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loadMacros( |
loadMacros( |
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| − | + | 'PGstandard.pl', |
|
| − | + | 'MathObjects.pl', |
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| − | + | 'answerComposition.pl', |
|
| − | + | 'PGML.pl', |
|
| + | 'PGcourse.pl' |
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); |
); |
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| − | |||
TEXT(beginproblem()); |
TEXT(beginproblem()); |
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</pre> |
</pre> |
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<td style="background-color:#ffdddd;border:black 1px dashed;"> |
<td style="background-color:#ffdddd;border:black 1px dashed;"> |
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<pre> |
<pre> |
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| − | Context()->texStrings; |
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| + | BEGIN_PGML |
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| − | BEGIN_TEXT |
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| + | Express the function [` y = \sqrt{ x^2 + [$a] } `] |
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| − | Express the function \( y = \sqrt{ x^2 + $a } \) |
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| + | as a composition [` y = f(g(x)) `] of two simpler |
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| − | as a composition \( y = f(g(x)) \) of two simpler |
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| + | functions [` y = f(u) `] and [` u = g(x) `]. |
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| − | functions \( y = f(u) \) and \( u = g(x) \). |
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| + | |||
| − | $BR |
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| + | + [` f(u) = `] [_______________] |
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| − | $BR |
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| + | |||
| − | \( f(u) \) = \{ ans_rule(20) \} |
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| + | + [` g(x) = `] [_______________] |
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| − | \{ AnswerFormatHelp("formulas") \} |
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| + | |||
| − | $BR |
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| + | [@ helpLink('formula') @]* |
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| − | \( g(x) \) = \{ ans_rule(20) \} |
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| + | END_PGML |
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| − | \{ AnswerFormatHelp("formulas") \} |
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| − | END_TEXT |
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| − | Context()->normalStrings; |
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</pre> |
</pre> |
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<td style="background-color:#ffcccc;padding:7px;"> |
<td style="background-color:#ffcccc;padding:7px;"> |
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<td style="background-color:#ddddff;border:black 1px dashed;"> |
<td style="background-color:#ddddff;border:black 1px dashed;"> |
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<pre> |
<pre> |
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| − | Context()->texStrings; |
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| + | BEGIN_PGML_SOLUTION |
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| − | BEGIN_SOLUTION |
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| − | ${PAR}SOLUTION:${PAR} |
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Solution explanation goes here. |
Solution explanation goes here. |
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| − | END_SOLUTION |
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| + | END_PGML_SOLUTION |
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| − | Context()->normalStrings; |
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| − | |||
| − | COMMENT('MathObject version.'); |
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ENDDOCUMENT(); |
ENDDOCUMENT(); |
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Revision as of 12:33, 10 March 2023
Function Decomposition
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
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( 'PGstandard.pl', 'MathObjects.pl', 'answerComposition.pl', 'PGML.pl', 'PGcourse.pl' ); TEXT(beginproblem()); |
Initialization:
We need to include the macros file |
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 |
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT(); |
Solution: |
