Anything from simple 2D plots..... 
.....to texture mapped 3D objects can be created in graphing programs. (image from GraphingCalc v2.1) 
Peeking into the eternal abyss of the Rosenbrock banana function. 
Price / limitations  Ease of use 
Graphics Candy  Animation  Change function + range + detail level on main screen?  Change view on main screen  Viewing features for 3D mode 
Graphics Speed  Templates  Max dim.  Multiple functions simultaneously  Range features  Special features  Math symbols  
A & G Grapher (v5.7)  $29.95 (30 day trial)  Easy  Basic (2D; Isometric 3D; wireframe; polygon shading)  No  ~f  No  Poor + V. Clumsy (Tilt scene on x/y axis)  Very slow  2D/3D cartesian  3  Yes  Yes  Trace curve to find coords; rotate graph; matrix transformation; good axis options  +/*^ mod abs log ln squareroot sin cos tan asin acos atan 
Aepryus Graph (v1.0)  $30 (30 day trial)  Easy  Basic (2D; 3D; wireframe; plots; polygon shading)  Yes  ~f  No  Poor (Camera rotate; Couldn't rotate scene on 3D x+y axis  bugged)  Very fast  2D polar + 2D/3D cartesian + 3D cylindrical/spherical  3  No  Yes but bugged  Scripting  +/*^ sin cos tan sec csc cot asin acos atan sinh cosh tanh ln log exp sqrt abs 
GraphMath (v2.5)  $10 (30 day trial)  Easy  Above average (2D; 3D; wireframe; plots; polygon shading; fog/ambient/shiny effects)  No  No  No  Poor (Camera rotate)  Very fast  2D/3D cartesian  3  No  No  Autorotate  +/*^ abs atn cos exp int log rnd sin sqr tan sec csec ctan asin acos asec acsec actan sinh cosh tanh ctanh sech csech asinh acosh atanh asech acsech actanh 
Function Grapher (v3.1.6)  $34.95 (20 load ups)  Okayish  Excellent (All essentials + specular reflections; light positioning; gourad shading; textures; materials; pleasing colours etc.)  Yes  No  Yes  Okay (Rotate scene; Camera zoom+rotate)  Lightning  2D polar + 2D/3D cartesian + 3D cylindrical/spherical  3  Yes  Yes but not for the Z axis in 3D mode  Advanced axis settings + Table graphs + Color map + contour plot + vector plot + 2D stuff (Graphs of series+intersection; limits; stem+step plots; differential equations)  +/*^ abs atn cos exp int log rnd sin sqr tan sec csec ctan asin acos asec acsec actan sinh cosh tanh ctanh sech csech asinh acosh atanh asech acsech actanh 
GraphingCalc (v2.1)  $4.95 (limited functionality)  Super Easy  Good (2D; 3D; wireframe; polygon shading; awesome 'nebula textures'  Limited  Yes!  Yes  Okay (Rotate scene; Camera move in/out)  Greased Lightning  2D/3D cartesian  3  3 available  X and Y only  Able to compress/expand z axis (Bugs: Only four detail levels)  +/*^ sqrt ln log exp sin cos tan csc sec cot step sgn rect ramp tri sinc gaus 
AceIT Grapher (v2.0)  $24.99 (30 days)  Easy  Above average (2D; 3D; wireframe; solid wireframe; polygon shading; flexible lighting)  No  f+r  Sort of  Okay + Clumsy (Rotate scene on X+Z axis; Change projection)  Fast  2D polar+cartesian + 3D  3  No  Yes  Drawing of deriatives + tangents; extensive 2D graph analysis; up to 8 window views  +/*^ abs ceil deg exp fact floor int mod ln log logn pi rad rand sqr sqrt sin cos tan cot sec csc asin acos atan acot asec acsc sinh cosh tanh coth sech csch asinh acosh atanh acoth asech acsch 
MoNoon Grapher (v2.0)  $720$ (No limitations)  Super Easy  Basic (2D; 3D; wireframe; polgon shading  No  f+r  Yes  Poor (Rotate scene; Camera zoom)  Lightning  2D polar + 2D/3D cartesian + 3D cylindrical/spherical  3  No  Yes    ? 
3DMath Explorer (v3.1)  $45 (30 day trial)  Okay (cumbersome) 
Above average (2D; 3D; wireframe; polgon shading; fogging  No  f+r  Yes  Good (Rotate scene; Camera rotate; Camera move in/out)  Fast  3D cartesian  3 (no 2D)  No  X and Y only  Display values + fourview + extensive grid support + multiple sample shapes  +/*^ logicfunctions mod div fact ceil floor int round abs sgn heav zero log ln sqrt sqr exp sin cos tan cotan sec cosec ph arcsin arccos arctan arccot arcsec arccosec sinh cosh tanh coth sech cosech arcsinh arccosh arctanh arccoth arcsech arccosech 
GraphCalc (v4.0.1)  Free  Easy  Above average (2D; 3D; wireframe with polgon shading; colour graduation)  No  No  Yes  Okay (Rotate scene; Camera move in/out)  Lightning  2D/3D cartesian + polar  3  610 available  X and Y only  Scripting + Extensive 2D graph analysis + grid features  ? 
A & G Grapher (v5.7)  $30This was the slowest by far out of all the graphers. Especially weird considering it has a stat on the main window giving pixels per second  you wouldn't think they would care about the speed, let alone want to show it off. Also annoying was the cumbersome camera features. It's not at all easy to get the right view should you need it. Other than that, it was easy to use, and has some neat features like curve tracing and multiple simultaneous functions displayed at once. The Rosenbrock banana function looks a mess to right... 

Aepryus Graph (v1.0)  $30Interesting program, but I could never change the camera view for some reason. Still, it's nippy, allows scripting and animation! 

GraphMath (v2.5)  $10The Rosenbrock function proved too much for GraphMath as you can painfully see to the right. Unfortunately, GraphMath also has very few features compared to the others reviewed here. For instance, the only thing you can do with the view is rotate the camera on the Y! Its saving grace is the low price tag, and the semi nice renderings (bottomright). 

Function Grapher (v3.1.6)  $35Apart from 3DMath Explorer, possibly the most professional program here, with tasty graphics, speed, and a wide range of features for the more discerning grapher, including color maps and graph analyses. One of my main gripes is how it's not possible to change the function, ranges or detail level on the main screen. It also does an okay job of the Rosenbrock function. Well it did after I divided the function by around 100 so that it wouldn't crash! However, one can't move the camera into the 'valley' part, because only camera 'zooming' is allowed, and of course, that's not the same as "moving forwards/backwards". 

GraphingCalc (v2.1)  $5The fastest out of all the programs here, GraphingCalc also sports some terrific GFX (see right). Also the second cheapest program in the running. Unfortunately, the demo is limited, and is more of a slideshow job. Nevertheless you can't go wrong for $5! The function, range and other important settings are in the main window which is good. A pity there's only 4 detail levels however. Not sure what it does with the Rosenbrock function until I test out the full version. 

AceIT Grapher (v2.0)  $25Not allowing you to navigate the graph with the mouse is a royal pain. Still, features such as the the flexible lighting and extensive 2D graph analysis help. The Rosenbrock function renders okayish, but you can't get close up! 

MoNoon Grapher (v2.0)  $720Feature wise, this is poor, but it's saved by the speed, ease of use, and ability to rotate the scene with the mouse. The Rosenbrock function is a mess to the right, unless you divide the function by a 100 or so, where it's a bit more acceptable. 

3DMath Explorer (v3.1)  $45The most expensive grapher at $45, and I had severe problems trying to get results out of it (the 'Apply' button is often blanked out). However, when it works, it works quite nicely as can be seen by the accompanying graphics. Just like GraphingCalc, it also allows you to move the camera into the scene  something which gives us a much better view of the Rosenbrock's function 'valley'. Features such as the fourview, extensive grid support, and multiple sample shapes also help. 

No 2D 
GraphCalc (v4.0.1)  FreeHey it's free! That's pretty rare these days. But how does the program compare to the rest? Well, the answer is pretty well actually. It's fast, allows scripting, 2D graph analysis, plus the rendering and navigation of the camera is also okay! The Rosenbrock function is handled reasonably well, but because the camera is unable to be rotated on the X and Y, one is forced to rotate the scene, which results in the slanted perspective. One can't complain at the egg crate though! 
