Graphs in a Table

Creating a set of graphs and displaying the options in a table.

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',     'PGML.pl',
    'PGtikz.pl',         'parserPopUp.pl',
    'PGchoicemacros.pl', 'PGcourse.pl'
);

Preamble

The PGtikz.pl macro is used to generate the graph, the parserPopUp.pl macro is used for a pop up (select) answer, the niceTables.pl macro (loaded automatically via PGML.pl) is used for layout, and the PGchoicemacros.pl macro provides the shuffle and invert functions.

@eqn_plot = ('-exp(\x)', 'exp(-\x)', '-exp(-\x)', 'exp(\x)');

# The tex form of the functions.
@eqn = ('y = -e^{x}', 'y = e^{-x}', 'y = -e^{-x}', 'y = e^{x}');

# Alternate text for each image.
@alt_text = (
    'A graph that starts close to and below the x-axis on the left '
        . 'and decreases to the right, decreasing more rapidly as '
        . 'it continues to the right.',
    'A graph that starts in the extreme upper left and decreases toward the '
        . 'x-axis, decreasing less rapidly as it continues to the right.',
    'A graph that starts in the extreme lower left and increases toward the '
        . 'x-axis, increasing less rapidly as it continues to the right.',
    'A graph that starts close to and above the x-axis on the left, '
        . 'and increases to the right, increasing more rapidly as '
        . 'it continues to the right.',
);

for my $i (0 .. 3) {
    $graph[$i] = createTikZImage();
    $graph[$i]->tikzLibraries('arrows.meta');
    $graph[$i]->BEGIN_TIKZ
\tikzset{>={Stealth[scale = 1.5]}}
\filldraw[
    draw = LightBlue,
    fill = white,
    rounded corners = 10pt,
    thick,
    use as bounding box
] (-3, -3) rectangle (3, 3);
\draw[->] (-3, 0) -- (3, 0) node[above left, outer sep = 3pt] {\(x\)};
\draw[->] (0, -3) -- (0, 3) node[below right, outer sep = 3pt] {\(y\)};
\draw[DarkBlue, thick] plot [smooth, domain = -3:3]
    (\x, {$eqn_plot[$i]});
END_TIKZ
}

$k = random(0, 3);

@perm     = shuffle(4);
@graph    = @graph[@perm];
@alt_text = @alt_text[@perm];
@inv      = invert(@perm);

@letters = ('A', 'B', 'C', 'D');
$popup   = DropDown(~~@letters, $letters[ $inv[$k] ]);

Setup

First, @eqn_plot, @eqn, @alt_text, and @graph arrays are defined containing the form of each equation for the TikZ graph, the TeX form of each equation, alternate text descriptions of the graphs for accessibility, and the TikZ graph for each equation. Because the graphs are shuffled and the correct graph picked randomly, the four arrays must be in the same order. Then one equation is picked at random (using $k) to be the correct choice. The graphs are shuffled using a permutation, and the inverse permutation used to recall the correct answer in the answer evaluation section.

If, instead, there were six graphs and it were desired to organize the graphs into three columns the tex_size would need to be adjusted. However, you are strongly discouraged from using more than three columns of graphs, because the graphs would need to be scaled down so much that they would become unreadable (especially in TeX mode).

BEGIN_PGML
Consider the exponential equation [`[$eqn[$k]]`].  Sketch a graph of this
equation on paper without using a calculator.

Which graph below most closely matches the graph you drew? [_]{$popup}

[#
    [.
        [#
            [.A.]*
            [.[![$alt_text[0]]!]{$graph[0]}.]
        #]*{ padding => [ 0, 0.1 ] }
    .]
    [.
        [#
            [.B.]*
            [.[![$alt_text[1]]!]{$graph[1]}.]
        #]*{ padding => [ 0, 0.1 ] }
    .]*

    [.
        [#
            [.C.]*
            [.[![$alt_text[2]]!]{$graph[2]}.]
        #]*{ padding => [ 0, 0.1 ] }
    .]
    [.
        [#
            [.D.]*
            [.[![$alt_text[3]]!]{$graph[3]}.]
        #]*{ padding => [ 0, 0.1 ] }
    .]
#]*{ align => 'cc' }
>>(Click on a graph to enlarge it.)<<
END_PGML

Statement

The LayoutTable method provided by niceTables.pl is used via its PGML syntax to organize the graphs into columns. See Layout Table for a more detailed example of how to do this.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.