There is a global pgfplots option for this. I think it is
"clipped=false". But if you use that, there will be an unwanted side
effect.
A pgfplots image is some default width, I forget what, but lets say
300pt. Right now, that 300pt is aligned with the axis width. Anything
that extends past, like the "^2" in that label is just not part of the
image. If you use clipped=false, then the width is still going to be
300pt, but everything is scaled down until that "^2" fits within that
width. In some images, that's fine. Here, alongside other similar
graphs, that will not look ideal.
Re:accessibility, a caption or other text with the function is not
enough on its own. The complete information about the bounds of the
shaded region is needed. Like in #5, saying its the region bounded
below by the x-axis, to the left by x=1, to the right by x=2, and
above by y=x. Probably that belongs in the alt test (PTX
"description").
I'm not feeling sure about things, but right now I would change the
labels like "y=x^2" to be anchored and positioned differently. So for
example, at (0.5,2.75), with a southwest anchor.
And only do this where immediately necessary. There is a discussion
that is formulating how to make tikz diagrams in a way that leads to
more accessible svgs that can be navigated. Something that would
clearly tell someone that "y=x^2" is a label for that curve element,
not just text floating in the image. If that gets worked out (and
someone has some time to spend, or a paid student to assign work to)
then it could be a larger project.
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