Well, no, in this scenario, it is actually the function (in your words, the graph of the function) that is convex. A 2D example would be y = x^2 (a parabola), which is a convex function. A 3D example would be a paraboloid function, which is also a convex function.
The "volume" (or "area" in the 2D case) above the graph is called an epigraph.
Convex sets are more abstract in meaning, but in general in means can draw a straight-line between any two points in the region without going outside of the region.
Perhaps your notion of convexity comes from a mental idea of the shapes of convex and concave lenses? Those are good visualizations but in mathematics, convexity has a subtler, more rigorous meaning. With this rigorous meaning comes many nice mathematical properties that make optimizing them easier than nonconvex functions.
The "volume" (or "area" in the 2D case) above the graph is called an epigraph.
One property of convex functions is that their epigraphs are convex sets (note the word "sets" this time). https://en.wikipedia.org/wiki/Epigraph_(mathematics)
Convex sets are more abstract in meaning, but in general in means can draw a straight-line between any two points in the region without going outside of the region.
Perhaps your notion of convexity comes from a mental idea of the shapes of convex and concave lenses? Those are good visualizations but in mathematics, convexity has a subtler, more rigorous meaning. With this rigorous meaning comes many nice mathematical properties that make optimizing them easier than nonconvex functions.