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EXTEND 5-3
Graphing Technology Lab
Inverse Functions and Relations
You can use a TI-83/84 Plus graphing calculator to compare a function and its inverse using tables
and graphs. Note that before you enter any values in the calculator, you should clear all lists.
Graph
f
(
x
)
=
{(1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12)} and its inverse.
Step 1
Enter the
x
-values in
L1
and the
y
-values in
L2
. Then graph the function.
Step 2:
keystrokes
:
1
2
3
4
5
6
2
4
6
8
10
12
[STAT PLOT]
Adjust the window to reflect the domain and range.
Step 2
Define the inverse function by setting
Xlist
to
L2
and
Ylist
to
L1
.
Then graph the inverse function.
keystrokes
:
[STAT PLOT]
[L2]
[L1]
Step 3
Graph the line
y
=
x
.
keystrokes
:
C07-003A-888482-A
[0, 14] scl: 1 by [0, 14] scl: 1
Step 3:
C07-004A-888482-A
[0, 14] scl: 1 by [0, 14] scl: 1
Activity 1
Graph Inverses with Ordered Pairs
Graph
f
(
x
)
=
3
x
and its inverse
g
(
x
)
=
x
_
3
.
Step 1
Clear the data from Activity 1.
keystrokes
:
[STAT PLOT]
[QUIT]
Step 2
Enter
f
(
x
) as
Y1
,
g
(
x
) as
Y2
, and
y
=
x
as
Y3
. Then graph.
keystrokes
:
3
3
C07-005A-888482-A
[0, 14] scl: 1 by [0, 14] scl: 1
Activity 2
Graph Inverses with Function Notation
Exercises
Graph each function
f
(
x
) and its inverse
g
(
x
). Then graph (
f
◦
g
)(
x
).
1.
f
(
x
)
=
5
x
2.
f
(
x
)
=
x
-
3
3.
f
(
x
)
=
2
x
+
1
4.
f
(
x
)
=
1
_
2
x
+
3
5.
f
(
x
)
=
x
2
6.
f
(
x
)
=
x
2
-
3
7.
What is the relationship between the graphs of a function and its inverse?
8.
MAKE A CONJECTURE
For any function
f
(
x
) and its inverse
g
(
x
), what is (
f
◦
g
)(
x
)?
336
|
Extend 5-3
|
Graphing Technology Lab: Inverse Functions and Relations