Using the When Function

For more information, look at p. 206 of the 89 manual. (The internet address of the manual download site for TIis:
http://education.ti.com/educationportal/appsdelivery/download/download_eula.jsp?cid=us&displayMode=G&applicationid=6129&contentpaneid=17
The syntax for two cases is:
when(condition, trueExpression, falseExpression)
Say case I is f(x) = 2x + 1, if x 3, and case II is f(x) = x - 7, if x < 3. You would type:
y1 = (x 3, 2x + 1, x - 7)
The reason is:
When x 3 is true, you want y to be 2x + 1.
When x 3 is false, i.e. when x < 3, you want y to be x - 7.
Hope this helps.
AS
PS The syntax for 3 cases is much harder but I'm not covering those problems anyway.

Using the When Function

To define a two-piece function, use the syntax:

when(condition, trueExpression, falseExpression)

For example, suppose you want to graph a function with two pieces.

For three or more pieces, you can use nested when functions.

When: Use expression:

x < 0 Mx

x | 0 5 cos(x)

In the Y= Editor: The function is “pretty

printed” in this form.

Enter the function in this

form.

Additional Graphing Topics 477

Note: To enter when, type it or use the CATALOG.

where:

Nested functions quickly become complex and difficult to visualize.

Using a Multi-Statement, User-Defined Function

For three or more pieces, you may want to create a multi-statement, user-defined

function.

When: Use expression:

x < Mp 4 sin(x)

x | M p and x < 0 2x + 6

x | 0 6 – x2

In the Y= Editor:

y1(x)=when(x<0,when(x< M p,4ùsin(x),2x+6),6Nx^2)

This nested function is in effect when x<0.

Additional Graphing Topics 478

For example, consider the previous three-piece function.

Note: For information about similarities and differences between functions and

programs, refer to Programming.

A multi-statement, user-defined function can have many of the control and decisionmaking

structures (If, ElseIf, Return, etc.) used in programming. When creating the

structure of a function, it may be helpful to visualize it first in a block form.

Ê Func and EndFunc must begin and end the function.

When entering a multi-statement function on the Y= Editor or Home screen, you must

enter the entire function on a single line.

When: Use expression:

x < Mp 4 sin(x)

x | M p and x < 0 2x + 6

x | 0 6 – x2

Ê

Ê

Func

If x< M p Then

Return 4ùsin(x)

ElseIf x>=-p and x<0 Then

Return 2x+6

Else

Return 6–x^2

EndIf

EndFunc

Additional Graphing Topics 479

From the Home Screen or a PrograFrom Program

From the Home screen, you can also use the Define command to create a multistatement,

user-defined function.

Information is available on copying a function from the Home screen to the Y= Editor.

From the Program Editor, you can create a user-defined function. For example, use the

Program Editor to create a function named f1(xx). In the Y= Editor, set y1(x) = f1(x).

Example (Source: Internet page http://www.batesville.k12.in.us/Physics/CalcNet/Calculator/ti_89/piecewise_fn.htm)

A complication is that this function is not defined for x < 0. It can be accurately represented on the TI-89 using the following nested function:

The last term, "1/0", assures that the value of the function will be undefined whenever x is less than zero.

THE BATESVILLE WEB PAGE HAS MANY HINTS FOR THE EASIER PROBLEMS AS WELL INCLUDING USE OF THE VERTICAL BAR | .