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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:
2
3; 2
() 2 ; 2 1
3;1
xx
fx x x
xx
+<−
=− −≤≤
−≥
To graph this we need to enter it into the SYMB view as
three separate functions:
F1(X)=(X+3)/(X < -2)
F2(X)=(X
2
-2)/(X ≥ -2 AND X ≤ 1)
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.
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