GraphShading.pg

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

$graph = createTikZImage();
$graph->tikzLibraries('arrows.meta');
$graph->BEGIN_TIKZ
\tikzset{>={Stealth[scale = 1.5]}}
\filldraw[
    draw = LightBlue,
    fill = white,
    rounded corners = 10pt,
    thick,use as bounding box
] (-6, -2) rectangle (6, 8);
\begin{scope}
    \clip[rounded corners = 14pt] (-6, -2) rectangle (6, 8);
    \draw[ultra thin] (-6, -2) grid (6, 8);
\end{scope}
\draw[->, thick] (-6, 0) -- (6, 0) node[above left, outer sep = 3pt] {\(x\)};
\foreach \x in {-5, ..., -1, 1, 2, ..., 5}
    \draw (\x, 5pt) -- (\x, -5pt) node[below] {\(\x\)};
\draw[->, thick] (0, -2) -- (0, 8) node[below right, outer sep = 3pt] {\(y\)};
\foreach \y in {-1, 1, 2, ..., 7}
    \draw (5pt, \y) -- (-5pt, \y) node[left] {\(\y\)};
\filldraw[draw = blue, fill = blue!50!white, fill opacity = 0.5]
    ({$a + 1}, 0) -- ({$a + 1}, {$b + 1})
    -- plot[domain = {$a + 1}:{$a + 4}, samples = 100] (\x, {$b + sqrt(\x - $a)})
    -- ({$a + 4}, 0) -- cycle;
\draw[blue, ultra thick, ->]
    plot[domain = {$a}:6, samples = 100] (\x, {$b + sqrt(\x - $a)});
END_TIKZ

$altText =
    "The graph of f(x) is shown starting at the point ($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.";

Setup

A randomly transformed version of sqrt(x) is created as the function with a reasonably straightforward answer.

The graph is created with PGtikz.pl, a robust plotting package. The shading in done with the \filldraw command with the fill opacity = 0.5. Also note that one of the sides of the filled area is the square root function.

Graph Shading (tikz)

Complete Code

POD for Macro Files

PG problem file

Explanation