HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010

Piecewise defined functions

It is possible to graph piecewise defined functions using the Function aplet, although it involves literally

splitting the function into pieces.

⎧

x + 3 ; x <− 2

⎪

For example:

fx()=

⎨

− 2 ; − 2 ≤ x ≤ 1

⎪

−

x ; x

≥

⎩

To graph this we need to enter it into the

SYMB view as

three separate functions:

F1(X)=(X+3)/(X < -2)

F2(X)=(X2-2)/(X ≥ -2 AND X ≤  1)

F3(X)=(3-X)/(X

≥ 1)

Note: The

AND function can be found on top of the (-) key.

-2 AND X ≤

The reason why this works is that the

(X < -2) and the (X ≥ 1) expressions are evaluated as being

either true (which for computers has a value of 1) or false (which has a value of 0).

By dividing by this domain expression we are effectively dividing by 1

inside the range (with no effect) or dividing by zero outside the domain

(making the function undefined). This can be seen in the

NUM view to

the right. Since undefined values are not graphed, this produces the

desired effect.