## DESCRIPTION ## Differential calculus: dynamically generated graph of a function with shading ## ENDDESCRIPTION ## KEYWORDS('precalculus', 'dynamic graph with shading') ## 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", "AnswerFormatHelp.pl", "PGgraphmacros.pl", "unionTables.pl", ); TEXT(beginproblem()); \$refreshCachedImages = 1; ############################################## # Setup Context("Numeric"); \$a = random(0,3,1); \$f = Formula("sqrt(x)+\$a"); \$answer = Compute("(2/3) * (4^(3/2) - 1) + 3*\$a"); # # Graph canvas # \$gr = init_graph(-5,-5,5,5,grid=>[10,10],axes=>[0,0],pixels=>[300,300]); # # Graph labels # \$gr->lb('reset'); foreach my \$j (1..4) { \$gr->lb( new Label(-4.7, \$j, \$j,'black','center','middle')); \$gr->lb( new Label(-4.7, -\$j,-\$j,'black','center','middle')); \$gr->lb( new Label( \$j,-4.7, \$j,'black','center','middle')); \$gr->lb( new Label( -\$j,-4.7,-\$j,'black','center','middle')); } \$gr->lb( new Label(4.7,0.2,'x','black','center','middle')); \$gr->lb( new Label(0.2,4.7,'y','black','center','middle')); # # Define new graph colors # \$gr->new_color("lightblue", 214,230,244); # RGB \$gr->new_color("darkblue", 100,100,255); \$gr->new_color("lightgreen",156,215,151); \$gr->new_color("darkgreen", 0, 86, 34); \$gr->new_color("lightred", 245,234,229); # light red-purple \$gr->new_color("darkred", 159, 64, 16); # red-brown # # Choose colors # \$light = "lightblue"; \$dark = "darkblue"; # # Graph the function and the filled region # add_functions(\$gr, "\$f for x in <0,5> using color:\$dark and weight:2"); \$gr->moveTo(1,\$a+1); \$gr->lineTo(1,0,\$dark,2); \$gr->lineTo(4,0,\$dark,2); \$gr->lineTo(4,\$a+2,\$dark,2); \$gr->fillRegion([1.1,0.1,\$light] ); ############################################# # Main text Context()->texStrings; BEGIN_TEXT \{ ColumnTable( "Use the graph to find the area of the shaded region under \( f(x) = \$f \). \$BR \$BR Area = " . ans_rule(20).\$SPACE. AnswerFormatHelp("numbers") , image( insertGraph(\$gr),height=>300,width=>300,tex_size=>800 ). \$BR.\$BCENTER. \$BR. "Graph of \( y = f(x) \)". \$ECENTER , indent => 0, separation => 30, valign => "TOP" ) \} END_TEXT Context()->normalStrings; ############################################### # Answer evaluation \$showPartialCorrectAnswers = 1; ANS( \$answer->cmp() ); ############################ # Solution Context()->texStrings; BEGIN_SOLUTION \${PAR}SOLUTION:\${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();