I was trying hard to find a alternative for showing mathematical graphs on my site. I want a grapher designed for plotting math equations (not statistical charts) and crap free.
I'm using a shared hosting, GNUplot + Simple PHP interface is not the most simple choice, especially the interface is far away from complete, more of a proof of concept script.

webMathematica, well, the Amateur version is free, but requires Premier Service, which requires a mathematica license. Let's say I brought mathematica student edition for $129 just to get the license and then pay for premier service to get my "free webMathematica amateur", that cost more than 2 years of quality hosting on site5. Other than it's expensiveness, it's totally amazing because it's the web front end of Mathematica.

If you have mathematica on your server, you can use WITM as a front end, or write your own [there's a command line version of mathematica comes with your beloved $129]. Remember to make cache system. Trust me, plotting the factorial from 1 to 10^5 is not cpu friendly. I will write about that really soon.

openPlaG is simple to use and take less than 1 minute to install (or even less.. download.. extract) and free. Over 150 built in math functions, include derivative and integral. But implemented in PHP result it's slowness. Write a cache module will avoid the problem of generating images on the fly with a interpreting language.

But openPlaG is only a back up for what I'm really using right now, a duplicate of Walter Zorn's Online Function Grapher.

It uses almost no server CPU (except output the js file) when compared with openPlaG. I believe it's the best choice for anyone who don't have the money, the time and the CPU. In the Drupal implementation [mathfilter], it is iframe a php file on the server, increases some CPU usage.

Calc5's graph calculator would be exactly what I would like to use to show graphs on this site. Compare to Walter's, this script uses canvas, and easy to zoom in/out, drag the plot to move around like in Google map. too bad there is no "embed this graph" link anywhere and does not show the corrdinate of the mouse either.

JS masters really can make a graphing calculator in JS and save all mathematicians.