How to make an Illustrator file “higher resolution”

I was given an illustrator file, but all the curves on the artwork are jagged. I've tried "rasterizing" and exporting by increasing the size of the image. I don't know what else to do or what I'm doing wrong.

My understanding is the beauty of Illustrator is that it's all done mathematically, so I can scale it up to infinity and it will be perfect (more or less). And that lines are drawn that way also, so they should be (or can be) infinitely smooth if they want to be.

Here's what I have right now:

Here's what I have with the image selected showing the plot lines:

And a zoomed in view:

*I'm not experienced in Illustrator at all; I only know whatever I can carry over from moderate Photoshop experience.