# TI-83 Tutorial

## Graphing Piecewise Defined Functions

The goal is to graph the following function on your TI-83, and to have the individual pieces appear together.

Use the key to get to the function editor, and then enter the functions.

### Step 1

Enter the function y1 = .5x + 4, with the specified domain x < -2.
On your calculator, the entry for Y1 should look like this:
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|  Y1=(.5X+4)*(X<-2)                       |
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Note the term (X<-2) that restricts the domain.
The symbol "<" is found on the Test menu that you get to by using the sequence of keys.
The symbol "*" is the usual one for multiplication, and is entered by pressing the key.
Be sure to enter the negative sign with the key, rather than the key.

### Step 2

Enter the function y2 = 1 - x, with the specified domain -2 < x < 2.
The calculator screen should now look like this:
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|  Y1=(.5X+4)*(X<-2)                       |
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|  Y2=(1-X)*(-2<X)*(X<2)                   |
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The two terms (-2<X) and (X<2) are necessary to describe the inequality -2 < x < 2.

### Step 3

Enter the function y3 = .2(x-2)2 - 1, with the specified domain 2 < x.
The screen for the function editor should now look like this.
     __________________________________________
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|  Y1=(.5X+4)*(X<-2)                       |
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|  Y2=(1-X)*(-2<X)*(X<2)                   |
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|  Y3=(.2(X-2)^2-1)*(2<X)                  |
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Now press the key. You should see a graph that has been defined in three pieces. Two of the pieces are straight lines, and the third is part of a parabola that is concave up.