Change > Per step
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Theory

Take a look at the applet: ??

Here you see the graph of a function y = f ( x ) on [–2,4].
If you let x increase in steps of 1 , you can see the value of the function f ( x ) increase or decrease. You can track these changes with the help of a table, and then draw the corresponding diagram of increments.

Hier zie je de grafiek van een functie y = f ( x ) op [–2,4].Als je de waarden van x met een vastestapgrootte h laat toenemen, kun je daarbij een tabel maken van de toenames Δ y van de functiewaarden.

WIth h = 1 you get the following table:

x –2 –1 0 1 2 3 4
y 26 42 46 44 42 46 64
∆y 16 4 –2 –2 4 16

Draw the corresponding diagram of increments next to the table.
The change at every step is always
Δ y = f ( x ) - f ( x - h ) .
With h = 1 these equations simplify to
Δ y = f ( x ) - f ( x - 1 ) .
The latter is useful if you know the function rule.
You can then use your graphing calculator and enter Y1=f(X) en Y2=Y1(X)–Y1(X–1), with f as the given function. This will give you the table of increments.
The calculator unfortunately cannot produce the sort of diagram of increments shown here.

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