jj3.pg

## DESCRIPTION
## Precalculus: Exponential and Logarithm Functions
## ENDDESCRIPTION

## Tagged by cmd6a 3/12/06

## DBsubject(Algebra)
## DBchapter(Exponential and logarithmic expressions and functions)
## DBsection(Graphs)
## Institution(ASU)
## MLT(Expo_match_graphs)
## Level(2)

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

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

TEXT(beginproblem());

$showPartialCorrectAnswers = 0;
install_problem_grader(~~&std_problem_grader);

$a = random(2,7);
$b = random(2, 8); 
$ym = max(10, $a+$b);

$graph1 = init_graph(-3,-1,3,$ym,
   'axes'=>[0,0],
   'ticks'=>[6,$ym+1]);

$graph2 = init_graph(-3,-1,3,$ym,
   'axes'=>[0,0],
   'ticks'=>[6,$ym+1]);

$graph3 = init_graph(-3,-$ym,3,1,
   'axes'=>[0,0],
   'ticks'=>[6,$ym+1]);

$graph4 = init_graph(-3,-1,3,$ym,
   'axes'=>[0,0],
   'ticks'=>[6,$ym+1]);

plot_functions( $graph1, 
"$a^x for x in <-3, 3> using color:blue and weight:2");

plot_functions( $graph2, 
"$a^(-x) for x in <-3, 3> using color:blue and weight:2");

plot_functions( $graph3, 
"-($a^x) for x in <-3, 3> using color:blue and weight:2");

plot_functions( $graph4, 
"$a^x+$b for x in <-3, 3> using color:blue and weight:2");

for $j1 (-6..5) {
$j = $j1/2;
$j2 = $j+0.25;
plot_functions( $graph4, 
"$b for x in <$j, $j2> using color:black and weight:1");
}

$ml = new_match_list();
$ml->qa("\($a^x\)", image(insertGraph($graph1),
    alt=>"Exponential decay curve y = a^(-x) decreasing from upper left to lower right, approaching the x-axis as x increases."
),
"\($a^{-x}\)", image(insertGraph($graph2),
    alt=>"Exponential decay curve of a^(-x), decreasing from upper left to lower right, approaching the x-axis as x increases."
),
"\(-$a^x\)", image(insertGraph($graph3),
    alt=>"Exponential function y = a^x + b shifted upward, with horizontal dashed line indicating the asymptote at y = b."
),
"\($a^x+$b\)", image(insertGraph($graph4),
    alt=>"Exponential function shifted up, showing y = a^x + b with horizontal asymptote at y = b indicated by dashed segments."
));
$ml->choose(4);

BEGIN_TEXT
For each function, enter the letter of the matching graph below,
$BR$BR
 \{ $ml->print_q() \}
$BR$BR
$BBOLD Note:$EBOLD you can get a larger view of any graph by clicking on it.
$BR$BR
\{ $ml->print_a() \}
END_TEXT

ANS(str_cmp($ml->ra_correct_ans()));

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