11-12 Applications
The test functions of the TI.80 can be used to build piecewise defined functions.
Define and graph this piecewise defined function.
f(x)=
xñ,for x≤3
1.5x+1, for 3<x<5
6ìx, for x≥5
The TEST functions, which return 1 if true and 0 if false, can
be used to build piecewise defined functions. For example,
when x is 4 (x≤3) is false and will return 0.
Follow this procedure to solve the problem.
1. Press 3 and select FUNC.
2. Enter the first piece of the function in the Y= editor. This
piece is f(x)=xñ for x≤3. It is entered as (xñ)(x≤3). Yã is
then equivalent to xñ×1 for x≤3 and xñ×0 for x>3.
3. Add the second piece of the function in the Y= editor. This
piece is f(x)=1.5x+1 for 3<x<5. It is entered as
(1.5x+1)(3<x)(x<5).
When x is less than 3, the test (3<x) returns 0, and the test
(x<5) returns 1. In this case, the second piece of the
function is equivalent to (1.5x+1)×0×1, which is 0. Only
when both of these tests are true will the second piece of
this function be anything but 0.
Graphing a Piecewise FunctionProblem
Procedure