Graphing Calculator Lab
TI-73 EXPLORER
Function Machines
A function machine takes a value called the input and performs one or
more operations on it according to a rule to produce a new value
called the output.
Main IDEA
Illustrate functions using
technology.
Another way to write the rule of a function machine is as an algebraic
expression. For the function machine above, an input value of x
produces an output value of x + 3. You can use the TI-73 Explorer graphing
calculator to model this function machine.
Use a graphing calculator to model a function machine for the
rule x + 3. Then use this machine to find the output values for
the input values 2, 3, 4, 9, and 12.
The graphing calculator uses X for input and Y for output values.
Enter the rule for the function into the function list. Press
3 to
to access the function list. Then press
enter the rule.
Next set up a table of input and output values. Press
[TBLSET] to display the table setup screen. Press
to highlight Indpnt: Ask. Then press
to
highlight Depend: Auto.
Graphing
Calculators Indpnt means
independent variable
and is the input or
x-value. Depend
means dependent
variable and is the
output or y-value.
ccess the table by pressing
A
[TABLE]. The calculator
will display an empty function table.
ow key in your input values, pressing
N
one.
after each
Use a graphing calculator to model a function machine for each
of the following rules. Use the input values 5, 6, 7, and 8 for x.
Record the inputs and their corresponding outputs in a table.
a.
x - 4 d. x - 3
b. x + 5
c.
x-2
e.
f.
x·3
x · 2
Analyze the Results
1.
Examine the columns of inputs and outputs for Exercises a–d.
What pattern do you observe in the column of inputs? What
pattern do you observe in each column of outputs? 2.
How would each column of outputs change if the order of the
inputs was reversed to be 8, 7, 6, and 5? 3.
Examine the columns of inputs and outputs for Exercises e and f.
What patterns do you observe in the column of outputs? 4.
Compare the patterns you observed in Exercise 3 to the rules given
for Exercises e and f. What do you notice? MAKE A CONJECTURE Based on your observations from Exercises 1–4,
make a conjecture about the rule for each set of input and output
values. Explain your reasoning.
5. Input (x)
Output (y)
6. Input (x)
Output (y)
10
2
2
12
11
12
13
14
3
4
5
6
3
4
5
6
18
24
30
36