Classes       Function Emojis


        Expand your visual vocabulary. You probably already use hand signals for concave up, concave down, and horizontal line. Now try function emojis to mark and summarize a graph using emojis for positive, negative, and 0 slope and function values, concave up, concave down and a variety of does not exist. Use emojis when teaching the first and second derivatives, when introducing slope, increasing functions, concavity or to draw a possible function given only x-values and derivatives. See the forest by decreasing the detail in the trees.

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.


    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

Download Geometer's Sketchpad for Free!

  1. Edit a function as desired or use the one already on the sheet.
  2. Draw the blue dot on the x-axis to the desired position and note the change in x, function, derivative, and second derivative values.
  3. Select appropriate emoji(s) and move the emoji(s) to mark a desired characteristic of the function.

    Examples and a practice sheet follow. Enjoy.

  function, then some derivatives

none f f, f' f, f', f'' all
none f f, f' f, f', f'' all
none f f, f' f, f', f'' all

none f f, f' f, f', f'' all

Practice Problems & Answers

A harder problem, and answer A3.

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