8PA CRM 3.2 Lessons 1-2

Functions
Lesson 1: Exploring Relations
Math Nation - Unit 10, Lesson 1 - Volume 2

What are we going to learn today?

Benchmark(s):

MA.8.F.1.1

Learning Target(s):

❏

Recognize functions represented in different forms.

Integrated MTR(s):

MTR 2

Exploration: Representing Mathematical Rules and Relations

2. Work with your partner

to complete the
input-output table for
each of the following
rules.

The first row has been
completed as an
example.

Math Nation - Unit 10, Lesson 1 - Exploring Relations - Volume 2, PAGE 120

Rule

Table of Values

Input

Output

¾

7

2.35

42

−1

Input

Output

−12

−5

6

19

4. Work with your

partner to
complete the
mapping diagram
for each of the
following rules.

Math Nation - Unit 10, Lesson 1 - Exploring Relations - Volume 2, PAGE 120-121

Rule

Mapping Diagram

Relations can be represented using graphs.

For each relation below, its graph and mapping diagram are shown.

Math Nation - Unit 10, Lesson 1 - Exploring Relations - Volume 2, PAGE 122

A set of ordered pairs can also be used to represent a relation.

8. The ordered pairs shown below can be used to represent Relation A from

the previous table.

Write the set of ordered pairs that represents Relation B from the
previous table.

Math Nation - Unit 10, Lesson 1 - Exploring Relations - Volume 2, PAGE 122

What are the similarities

and differences

between representing a

relation in a mapping

diagram, a graph, and a

set of ordered pairs?

Next Page

Fill in the Blanks

Write the set of ordered pairs that represents Relation B from the previous table.

ex: (_,_)(_,_)...

Functions
Lesson 2: Identifying Domain and Range
Math Nation - Unit 10, Lesson 2 - Volume 2

What are we going to learn today?

Benchmark(s):

MA.8.F.1.1

Learning Target(s):

❏

Relate the domain and range to independent and dependent
variables in a relation.

❏

Identify the domain and range of a relation.

Integrated MTR(s):

MTR 7

Guided Instruction: Identifying the Domain and Range of a Relation

1. Consider the statements shown.

12 ÷ 3 = 4 because 12 = 4 · 3.

6 ÷ 0 = 𝑥 because 6 = 𝑥 · 0.

In the second statement, what value can be used in place of 𝑥 so that the
statement is true?

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 125

The inputs of a relation are described as its domain.

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 125

Sometimes one or more values are not allowed in the domain.

Think of the domain like places you are allowed to go…

Are there places you are not allowed to go?

Are there people who you try to keep out of your room?

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 125

2. Use the rule to complete the table of values to represent the relation described

by the rule and answer the subsequent questions.

a. Complete the table of values.

b. In this relation, _____ is not an

allowable input.

Therefore, the domain does
not include ____.

c. Work with your partner to

determine if there is another
input that is not allowable
for .

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 126

The domain of Rule A can be represented using inequalities for the input
values defined as 𝑥.

𝑥 > ____ or 𝑥 < ____

These two inequalities can also be written as one,

𝑥≠ ___.

The outputs of a relation are described as its range.

When is the inequality
symbol open to the left

versus right?

When is the inequality

symbol underlined

versus not underlined?

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 126

3. Use the rule to complete the mapping diagram and answer the subsequent questions.

a. Complete the mapping diagram.

b. Based on the rule, what

type of output values are
unattainable for this
relation?

c. Write an inequality to

represent the range of
this relation.

At times, the domain and range of a relation can be represented using a list of numbers.

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 127

4. For each relation, write the domain and range as a set of numbers.

Next Page

Multiple Choice

Select the DOMAIN as a set of numbers.

• -3 , -3 , -1 , -2.5

• -2 , 0 , 1.5 , 3

• -2 , 2 , -1 , 3

• -2 , -3 , 1.5 , 3

Multiple Choice

Select the RANGE as a set of numbers.

• -3 , -1 , 2.5

• -2 , -0 , 1.5 , 3

• -2 , 2 , -1 , 3

• -2 , -3 , 1.5 , 3

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 127

4. For each relation, write the domain and range as a set of numbers.

Next Page

Multiple Choice

Select the DOMAIN as a set of numbers.

• 1,-4, 4, 5, -1

• -1, 1, 4

• -4, 5

Multiple Choice

Select the RANGE as a set of numbers.

• 1,-4, 4, 5, -1

• -1, 1, 4

• -4, 5

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 127

There are also instances where the domain and range of a relation can be
represented by a compound inequality.

For example,
−4 ≤ 𝑥 ≤ ⅗

is a compound inequality that is read, “−4 is less than or equal to 𝑥, which is less

than or equal to ⅗ .” This inequality is true for any value of 𝑥 between −4 and ⅗ ,

including either of those values.

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 127

5. A graph is shown.

a. Represent the domain and range of the graph

using compound inequalities.

Domain: ___________
Range: ____________

b. Compare this graph to Relation A in the

previous problem. Discuss with your partner
why representing the domain and range of this
graph could not be done by writing the
elements of each in a list.

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 128

Try It: Identifying the Domain and Range of a Relation

1.

Identify the domain and range of each relation. Represent the domain as a list or using an
inequality.

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 128

Math Nation - Unit 10, Lesson 2 - Identifying Domain and Range - Volume 2, PAGE 128