flygraph.pg

## DESCRIPTION
## WeBWorK Demo 
## ENDDESCRIPTION

## KEYWORDS('demo')
## Tagged by jjh2b

## DBsubject('WeBWorK')
## DBchapter('Demos')
## DBsection('Problem')
## Date('')
## Author('')
## Institution('')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();
loadMacros(
  "PGstandard.pl",
  "PGchoicemacros.pl",
  "PGgraphmacros.pl",
  "PGcourse.pl"
);

$showPartialCorrectAnswers =0;

TEXT(beginproblem());
# Define the graph
$graph = init_graph(-4,-4,4,4,'axes'=>[0,0],'grid'=>[8,8]);


# create a scrambled list of colors and letters.
@colors = ("blue", "red", "green");
@slice = NchooseK(3,3);
@sc = @colors[@slice];  #scrambled colors
@sa = ('A','B','C')[@slice];
# Now we are ready to write the strings which define the function
$dom = 4;
$a=random(0, 6.3, .1);
$b=random(1.1, 1.5, .1);
$f = FEQ("sin($a+$b*cos(x)) for x in <-$dom,$dom>
using color:$sc[0] and weight:2");
$fp = FEQ("cos($a+$b*cos(x))*(-$b)*sin(x)  for x in <-$dom,$dom> using color=$sc[1] and weight:2");
$fpp = FEQ("-sin($a+$b*cos(x))*$b*$b*sin(x)*sin(x)+cos($a+$b*cos(x))*(-$b)*cos(x) for x in <-$dom,$dom> using color=$sc[2] and weight=2");

# Install the functions into the graph object.
($fRef,$fpRef,$fppRef) = plot_functions( $graph,
$f,$fp,$fpp
);

# create labels for each function
$label_point=-0.75;
$label_f = new Label ( $label_point, &{$fRef->rule}($label_point), 
$sa[0],$sc[0],'left');
$label_fp = new Label ( $label_point,&{$fpRef->rule}($label_point),
$sa[1],$sc[1],'left');
$label_fpp = new Label ( $label_point,&{$fppRef->rule}($label_point),
$sa[2],$sc[2],'left');   

# insert the labels into the graph
$graph->lb($label_f,$label_fp,$label_fpp);                 


# This inserts the graph and then asks three questions:
BEGIN_TEXT
\{ image(insertGraph($graph),
    alt=>"Three curves labeled A (blue), B (red), and C (green) showing a function and its first and second derivatives on the same coordinate plane."
) \} $PAR
Identify the graphs A (blue), B( red) and 
C (green) as the graphs of a function and its
derivatives (click on the graph to see an enlarged image):$PAR
\{ans_rule(4)\} is the graph of the function $PAR
\{ans_rule(4)\} is the graph of the 
function's first derivative $PAR
\{ans_rule(4)\} is the graph 
of the function's second derivative $PAR
END_TEXT
ANS(str_cmp( [@sa] ) );
&ENDDOCUMENT;