# 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 y_{1} = .5x + 4,
with the specified domain x < -2.

On your calculator, the entry for Y_{1} should look like this:
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| Y_{1}=(.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 y_{2} = 1 - x,
with the specified domain -2 < x < 2.

The calculator screen should now look like this:
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| Y_{1}=(.5X+4)*(X<-2) |
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| Y_{2}=(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 y_{3} = .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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| Y_{1}=(.5X+4)*(X<-2) |
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| Y_{2}=(1-X)*(-2<X)*(X<2) |
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| Y_{3}=(.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.

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