## DESCRIPTION ## Precalculus: function decomposition ## ENDDESCRIPTION ## KEYWORDS('precalculus', 'function decomposition') ## DBsubject('WeBWorK') ## DBchapter('WeBWorK Tutorial') ## DBsection('Fort Lewis Tutorial 2011') ## Date('01/30/2011') ## Author('Paul Pearson') ## Institution('Fort Lewis College') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') ########################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "answerComposition.pl", "AnswerFormatHelp.pl", ); TEXT(beginproblem()); ########################### # Setup Context("Numeric"); Context()->variables->add(u=>"Real"); $a = random(2,9,1);$f = Formula("sqrt(u)"); $g = Formula("x^2+$a"); ########################### # Main text 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; ############################ # Answer evaluation$showPartialCorrectAnswers = 1; COMPOSITION_ANS( $f,$g, vars=>['u','x'], showVariableHints=>1); ############################ # Solution Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();