Recall Algebra & Precalc Vocabulary
The use of function emojis began with the study of derivatives as used analyzing a function and sketching a curve. A list (in order from most important and earliest use to more advanced) of algebra & precalculus vocabulary sets the stage for calculus vocabulary which follows.

Analyticaly vs Numericaly vs Both & A Bit More
Traditionally (on paper and in books) topics in calc are examined analytically and numerically. Now with communciation on the web and in digital form, we have more room for communication and may use analytical and numeric and verbal and ... additional symbolic, graphic, notation  the emoji. Emojis are derivative dependant. See: Function & Graph Analysis  instructions on how to find extremes and perdict the future. 
SketchPad
An example of such a digital format is found in a Geometer's Sketchpad at fX.f'X.f''X.intX.gsp and at compositeFX.gsp

Instructions
Examples and a practice sheet follow. Enjoy.

www.mathnstuff.com/math/spoken/here/2class/420/420gspSUPPORT/emojis.htm 