DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'plots.pl', 'PGcourse.pl');


$a    = random(-4, 2);
$b    = random( 1, 4);
$g    = Compute("$b + sqrt(x - $a)")->reduce;
$area = Compute("3*$b + 14/3");

$plot = Plot(
    xmin        => -8,
    xmax        =>  8,
    ymin        => -2,
    ymax        =>  8,
    xtick_delta =>  1,
    ytick_delta => 2
);

$plot->add_function(
    $g, 'x', $a, 8,
    color        => 'blue',
    name         => 'A',
    fill         => 'xaxis',
    fill_min     => $a + 1,
    fill_max     => $a + 4,
    fill_color   => 'green',
    fill_opacity => 0.5
);

$altText =
    "The graph of f(x) is shown starting at the point ($a, $b) and increasing "
    . "to the right, sharply at first, and less sharply as it continues to the "
    . "right. The region from x = "
    . ($a + 1)
    . " to x = "
    . ($a + 4)
    . " that is above the x-axis and below the function is shaded.";

BEGIN_PGML
Use the graph to find the area of the shaded region under [`f(x) = [$g]`].

>>[![$altText]!]{$plot}{400}<<

>>Graph of [`y = f(x)`].<<

Area: [_]{$area}{15}
END_PGML

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();