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Piecewise defined functions
It is possible to graph piecewise defined functions using the Function aplet,
although it involves literally splitting the function into pieces.
For example:
=
f x
( )
To graph this we need to enter it into the SYMB view as
three separate functions:
F1(X)=(X+3)/(X < -2)
2
-2)/(X ≥ -2 AND X ≤ 1)
F2(X)=(X
F3(X)=(3-X)/(X ≥ 1)
Note: AND can be found on the (-) key.
The reason why this works is that the (X < -2)
and the (X ≥ -2 AND 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 the domain expression we are effectively dividing by 1 inside
the range (no effect) or dividing by zero outside the domain, making the
function undefined. Since undefined values are not graphed, this produces
the desired effect.
+
< −
x
3
;
x
2
−
− ≤ ≤
2
x
2
; 2
x
1
−
≥
3
x
;
x
1
85
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