In older Grapher versions, the image was copy and pasted using the screen resolution for the pasted resolution. This is normally 96 DPI. Grapher 12 increased this resolution to the default printer resolution for the pasted resolution. This is normally much higher and depends on the default printer specification. Typically, this is 300 DPI or higher.
If the copy/pasted Grapher image still looks too coarse, you can try changing the default printer printer quality. Alternatively, use the Paste Special option and paste as a bitmap or export the graph from Grapher and insert it into your other program.
Updated October 3, 2016