Take a look at the applet: ??
Here you see the graph of a function on [–2,4].
If you let increase in steps of , you can see the value of the function 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 functieop [–2,4].Als je de waarden vanmet een vastestapgrootte laat toenemen, kun je daarbij een tabel maken van de toenamesvan de functiewaarden.
WIth 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
.
With these equations simplify to
.
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 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.