Inverse of a Function

Create an Inverse

Station 1

Key Terms

Absolute value function

Exponential function

Inverse of a function

Linear function

Quadratic function

Reciprocal function

Your Task

For each of the following pairs decide:

o  Decide what function family the original is part of.

o  Tell how you know what kind of a function it is.

o  Write a rule for the function and graph it.

o  Create a new relation by exchanging the x and y values (the first one is started for you.) This is the inverse of the original.

o  What is the new relation?

o  Write a rule and graph the new relation.

Pair 1

Original / New
X / y / x / y
-4 / 12 / 12 / -4
-3 / 9 / 9 / -3
-2 / 6
-1 / 3
0 / 0
1 / -3
2 / -6
3 / -9
4 / -12

Pair 2

Original / New
X / y / x / y
-4 / 1
-3 / 2
-2 / 3
-1 / 4
0 / 5
1 / 6
2 / 7
3 / 8
4 / 9

Pair 3

Original / New
X / y / x / y
-4 / 3
-3 / 3
-2 / 3
-1 / 3
0 / 3
1 / 3
2 / 3
3 / 3
4 / 3

What do you notice about how the new graph and the original graph are related to each other?

Are there any places where either the original graph or the new graph has two points on the same vertical line?

Note anything else that you discovered in this activity.

Create an Inverse

Station 2

Key Terms

Absolute value function

Exponential function

Inverse of a function

Linear function

Quadratic function

Reciprocal function

Your Task

For each of the following pairs decide:

o  Decide what function family the original is part of.

o  Tell how you know what kind of a function it is.

o  Write a rule for the function and graph it.

o  Create a new relation by exchanging the x and y values (the first one is started for you.) This is the inverse of the original.

o  What is the new relation?

o  Write a rule and graph the new relation.

Pair 1

Original / New
X / y / x / y
-4 / 16 / 16 / -4
-3 / 9 / 9 / -3
-2 / 4
-1 / 1
0 / 0
1 / 1
2 / 4
3 / 9
4 / 16

Pair 2

Original / New
X / y / x / y
-4 / 12
-3 / 5
-2 / 0
-1 / -3
0 / -4
1 / -3
2 / 0
3 / 5
4 / 12

Pair 3

Original / New
X / y / x / y
-4 / 4
-3 / 1
-2 / 0
-1 / 1
0 / 4
1 / 9
2 / 16
3 / 25
4 / 36

What do you notice about how the new graph and the original graph are related to each other?

Are there any places where either the original graph or the new graph has two points on the same vertical line?

Note anything else that you discovered in this activity.

Create an Inverse

Station 3

Key Terms

Absolute value function

Exponential function

Inverse of a function

Linear function

Quadratic function

Reciprocal function

Your Task

For each of the following pairs decide:

o  Decide what function family the original is part of.

o  Tell how you know what kind of a function it is.

o  Write a rule for the function and graph it.

o  Create a new relation by exchanging the x and y values (the first one is started for you.) This is the inverse of the original.

o  What is the new relation?

o  Write a rule and graph the new relation.

Pair 1

Original / New
X / y / x / y
-4 / 8 / 8 / -4
-3 / 6 / 6 / -3
-2 / 4
-1 / 2
0 / 0
1 / 2
2 / 4
3 / 6
4 / 8

Pair 2

Original / New
X / y / x / y
-4 / 5
-3 / 3
-2 / 1
-1 / -1
0 / -3
1 / -1
2 / 1
3 / 3
4 / 5

Pair 3

Original / New
X / y / x / y
-4 / -4
-3 / -1
-2 / 2
-1 / -1
0 / -4
1 / -7
2 / -10
3 / -13
4 / -16

What do you notice about how the new graph and the original graph are related to each other?

Are there any places where either the original graph or the new graph has two points on the same vertical line?

Note anything else that you discovered in this activity.

Create an Inverse

Station 4

Key Terms

Absolute value function

Exponential function

Inverse of a function

Linear function

Quadratic function

Reciprocal function

Your Task

For each of the following pairs decide:

o  Decide what function family the original is part of.

o  Tell how you know what kind of a function it is.

o  Write a rule for the function and graph it.

o  Create a new relation by exchanging the x and y values (the first one is started for you.) This is the inverse of the original.

o  What is the new relation?

o  Write a rule and graph the new relation.

Pair 1

Original / New
X / y / x / y
-4 / 0.01 / 0.01 / -4
-3 / 0.03 / 0.03 / -3
-2 / 0.11
-1 / 0.33
0 / 1
1 / 3
2 / 9
3 / 27
4 / 81

Pair 2

Original / New
X / y / x / y
-4 / 0.25
-3 / 0.5
-2 / 1
-1 / 2
0 / 4
1 / 8
2 / 16
3 / 32
4 / 64

Pair 3

Original / New
X / y / x / y
-4 / -2.75
-3 / -2.5
-2 / -2
-1 / -1
0 / 1
1 / 5
2 / 13
3 / 29
4 / 61

What do you notice about how the new graph and the original graph are related to each other?

Are there any places where either the original graph or the new graph has two points on the same vertical line?

Note anything else that you discovered in this activity.

Create an Inverse

Station 5

Key Terms

Absolute value function

Exponential function

Inverse of a function

Linear function

Quadratic function

Reciprocal function

Your Task

For each of the following pairs decide:

o  Decide what function family the original is part of.

o  Tell how you know what kind of a function it is.

o  Write a rule for the function and graph it.

o  Create a new relation by exchanging the x and y values (the first one is started for you.) This is the inverse of the original.

o  What is the new relation?

o  Write a rule and graph the new relation.

Pair 1

Original / New
x / y / x / y
-4 / -0.25 / -0.25 / -4
-3 / -0.33 / -0.33 / -3
-2 / -0.5
-1 / -1
0 / ERROR
1 / 1
2 / 0.5
3 / 0.33
4 / 0.25

Pair 2

Original / New
x / y / x / y
-4 / -0.33
-3 / -0.5
-2 / -1
-1 / ERROR
0 / 1
1 / 0.5
2 / 0.33
3 / 0.25
4 / 0.20

Pair 3

Original / New
x / y / x / y
-4 / 0.75
-3 / 0.66
-2 / 0.5
-1 / 0
0 / ERROR
1 / 2
2 / 1.5
3 / 1.33
4 / 1.25

What do you notice about how the new graph and the original graph are related to each other?

Are there any places where either the original graph or the new graph has two points on the same vertical line?

Note anything else that you discovered in this activity.