Change > Per step
12345Per step

## Theory

Take a look at the applet: ??

Here you see the graph of a function $y=f\left(x\right)$ on [–2,4].
If you let $x$ increase in steps of $1$, you can see the value of the function $f\left(x\right)$ 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 $y=f\left(x\right)$op [–2,4].Als je de waarden van $x$met een vastestapgrootte $h$laat toenemen, kun je daarbij een tabel maken van de toenames $\Delta y$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
$\Delta y=f\left(x\right)-f\left(x-h\right)$.
With $h=1$ these equations simplify to
$\Delta y=f\left(x\right)-f\left(x-1\right)$.
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.