rich2.pg

## DESCRIPTION
## Algebra
## ENDDESCRIPTION

## Tagged by cmd6a 8/6/06

## DBsubject(Algebra)
## DBchapter(Functions)
## DBsection(Definition, concept)
## Institution(ASU)
## MLT(intgraph)
## Level(2)
## KEYWORDS('algebra','function','graph')

DOCUMENT();        # This should be the first executable line in the problem.

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

TEXT(beginproblem());
$showPartialCorrectAnswers = 0;

@x = (-.16,  0,  2,  4,  6,  8, 10,12,12.165); 
@y1 = (92.2, 92, 88, 86, 85, 88,94,99,99.2);
@y2 = (41.2, 41, 37, 34, 32, 35,39,44,44.2);
@y3 = (49.2, 49, 47, 44, 45, 47,50,51,51.2);
@y4 = (66.2, 66, 64, 61, 60, 62,66,68,68.2);
@y5 = (82.2, 82, 78, 75, 73, 74,77,82,82.2); 
@yy = (@y1, @y2, @y3, @y4, @y5);
@month = ('warm July','cool January', 'cool December', 'mild October', 'warm August');
@ymax = (100, 45, 55, 70, 85);
@ymin = (78, 28, 38, 53, 68);
@ax = (80, 30, 40, 55, 70);
for ($n=0; $n<=4; $n++) {
$d[$n] = $ymax[$n]-$ymin[$n];  }

$i = random(0,4);

if    ($i==0) {@y=@y1; @arr = (1, 2, 3, 4);  }
elsif ($i==1) {@y=@y2; @arr = (0, 2, 3, 4);  }
elsif ($i==2) {@y=@y3; @arr = (0, 1, 3, 4);  }
elsif ($i==3) {@y=@y4; @arr = (0, 1, 2, 4);  }
else          {@y=@y5; @arr = (0, 1, 2, 3);  }

for ($n=0; $n<=4; $n++) {

$graph[$n] = init_graph(-1,$ymin[$n],13,$ymax[$n],'grid'=>[ 14,$d[$n] ]);
$l1 = new Label(0.07, $ax[$n], "0",'black','left');
$l2 = new Label(12.07, $ax[$n], "12",'black','left');
$jj = 9*$n +1;
for ($j=1; $j<7; $j++) {
$k = $j+1; $kk = $jj + 1;
$a = ($yy[$kk]-$yy[$jj])/($x[$k]-$x[$j]);$b = $yy[$jj]-$a*$x[$j]; 
$f = "$a*x+$b for x in <$x[$j],$x[$k]> using color:blue and weight:2";
plot_functions($graph[$n], $f); 
$graph[$n]->stamps(closed_circle($x[$j],$yy[$jj],'red'));
$jj = $kk;  }
$graph[$n]->stamps(closed_circle($x[$k],$yy[$kk],'red'));
$graph[$n]->lb('erase');
# put in x-axis
$graph[$n]->h_axis($ax[$n], 'black');
# most of y-axis
$graph[$n]->moveTo(0, $ax[$n]+1); $graph[$n]->lineTo(0,$ymax[$n],'black');
#squiggle in y-axis
$graph[$n]->moveTo(0, $ymin[$n]); $graph[$n]->lineTo(0,$ax[$n]+.2,'black');
$graph[$n]->lineTo(.2,$ax[$n]+.3,'black');
$graph[$n]->lineTo(-.2,$ax[$n]+.6,'black');
$graph[$n]->lineTo(0,$ax[$n]+1,'black');
for ($ijk=$ax[$n]+2; $ijk<=$ymax[$n]-1; $ijk +=2) {
 $graph[$n]->lb( new Label(0, $ijk, $ijk,'black','right','middle'));
}
$graph[$n]->lb($l1, $l2); 
   }

@ym =  (0, 0, 4,4, 4, -4, -4,0,0 );
$herm = new Hermite(~~@x, ~~@y, ~~@ym);
$gr2 = init_graph(-1,$ymin[$i],13,$ymax[$i],
'grid'=>[14,$d[$i] ]);
new Fun($herm->rf_f,$gr2);

$gr2->lb('erase');
$l1 = new Label(0.07, $ax[$i], "0",'black','left');
$l2 = new Label(12.07, $ax[$i], "12",'black','left');
$gr2->lb($l1,$l2);
# put in x-axis
$gr2->h_axis($ax[$i], 'black');
# most of y-axis
$gr2->moveTo(0, $ax[$i]+1); $gr2->lineTo(0,$ymax[$i],'black');
#squiggle in y-axis
$gr2->moveTo(0, $ymin[$i]); $gr2->lineTo(0,$ax[$i]+.2,'black');
$gr2->lineTo(.2,$ax[$i]+.3,'black');
$gr2->lineTo(-.2,$ax[$i]+.6,'black');
$gr2->lineTo(0,$ax[$i]+1,'black');
for ($ijk=$ax[$i]+2; $ijk<=$ymax[$i]-1; $ijk +=2) {
 $gr2->lb( new Label(0, $ijk, $ijk,'black','right','middle'));
}



for ($j=1; $j<=7; $j++) {
$gr2->stamps(closed_circle($x[$j],$y[$j],'red'));  }

$m = new_multiple_choice();
$m->qa( "Which graph best represents the data?",image(insertGraph($graph[$i]),
    alt=>"Scatter plot showing seven data points of temperature T versus time t, with a squiggle break on the y-axis indicating a truncated scale."
) );
$m->extra(image(insertGraph($graph[$arr[0]]),
    alt=>"Scatter plot showing temperature readings in Fahrenheit versus time in hours, with seven data points plotted as red dots on a coordinate grid."
), 
image(insertGraph($graph[$arr[1]]),
    alt=>"Scatter plot showing temperature readings in degrees Fahrenheit versus time in hours, with data points plotted from midnight to noon."
), image(insertGraph($graph[$arr[2]]),
    alt=>"Scatter plot showing temperature readings in degrees Fahrenheit versus time in hours, with data points plotted at 2-hour intervals from midnight to noon."
), 
image(insertGraph($graph[$arr[3]]),
    alt=>"Scatter plot showing temperature readings in degrees Fahrenheit versus time in hours, with data points recorded every 2 hours from midnight to noon."
), 
image(insertGraph($gr2),
    alt=>"Scatter plot showing temperature readings in Fahrenheit versus time in hours, with seven data points marked from midnight to noon."
)   );


BEGIN_TEXT
Temperature readings $BITALIC T $EITALIC (in degrees Fahrenheit) were recorded every 2 hours from midnight to noon in Tempe, Arizona on a $month[$i] morning. The time $BITALIC t $EITALIC was measured in hours after midnight. 
$BR $BCENTER
\{ begintable(2 ) \}
\{row('time, $BITALIC t $EITALIC','Temp, $BITALIC T $EITALIC') \}
\{row($x[1],$y[1] ) \}
\{row($x[2],$y[2] ) \}
\{row($x[3],$y[3] ) \}
\{row($x[4],$y[4] ) \}
\{row($x[5],$y[5] ) \}
\{row($x[6],$y[6] ) \}
\{row($x[7],$y[7] ) \}
\{endtable()\}
$ECENTER
$BR
\{ $m->print_q() \}
$BR $BBOLD Note: $EBOLD Click on any graph to view a larger graph.
$BR
\{ $m->print_a() \}
$BR 


END_TEXT

ANS(radio_cmp( $m->correct_ans )   ) ;

ENDDOCUMENT();        # This should be the last executable line in the problem.