A function is a rule that turns input values into output values. For example, the function f(x) = 2·x + 3 is a rule that says “To get an output value, start with the input value, multiply it by 2, and then add 3 to the result.” To evaluate a function you follow the rule for a particular input value. For example, f(5) = 2(5) + 3 = 13.
There are three kinds of functions in Sketchpad:
•A symbolically defined function is defined by an algebraic rule.
•A derivative function is defined by finding the derivative of another function.
•A datadefined function is defined by the top stroke of a drawing or the top edge of a picture.
Once you've created a function, see Using Functions for information on the many ways you can use a function.
To define a new function symbolically, for example, f(x) = 2·sin(x), choose Number  New Function. This command opens Sketchpad’s Calculator to allow you to define how the function is calculated. To create a new function and plot it immediately, choose Graph  Plot New Function. To determine whether the function appears in y= notation or f(x) notation, choose the desired notation from the Calculator’s Equation popup menu. See also: 
To create a derivative function, select the function you want to differentiate and choose Number  Define Derivative Function. The derivative of a symbolicallydefined function is usually defined symbolically, as shown on the left. In rare cases of exceptionally complex symbolicallydefined functions, the derivative may be defined approximately. The derivative of a datadefined function (defined by a drawing or picture) is always defined approximately, as shown on the right.
To determine whether the function appears in y= notation or f(x) notation, set the desired notation for the parent function.

To create a datadefined function based on a drawing or picture, select the drawing or picture and choose Number  Define Function from Drawing. The function is defined by the top edge of the drawing or picture. To determine how much smoothing is applied to the function, choose Edit  Properties  Function. An unsmoothed function follows every pixel in the top edge of the drawing or picture; a smoothed function reduces the small variations. To determine whether the function appears in y= notation or f(x) notation, choose Edit  Properties  Function. 
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