1. {(27, -3), (8, -2), (1,-1), (0,0), (1,1), (8,2), (27,3)}

2. {(7, -3), (-5,-4), (8,0), (0,0), (-6,4), (-2,2), (-1,3)}

A. Determine whether the relation is function or not function.

B. Find the domain of the relation; and

C. Find the range of the relation.

To determine if the given sets of ordered pairs represent functions and to find their domains and ranges, we will follow these steps:

### Relation 1: \(\{(27, -3), (8, -2), (1, -1), (0, 0), (1, 1), (8, 2), (27, 3)\}\)

#### A. Determine if it is a function:
A relation is a function if each input (first element of the ordered pair) corresponds to exactly one output (second element of the ordered pair).

For Relation 1:
- The input 27 corresponds to -3 and 3.
- The input 8 corresponds to -2 and 2.
- The input 1 corresponds to -1 and 1.
- The input 0 corresponds to 0.

Since the inputs 27, 8, and 1 each correspond to more than one output, Relation 1 is **not a function**.

#### B. Find the domain:
The domain is the set of all possible inputs (first elements) of the ordered pairs.

For Relation 1:
\[
\text{Domain} = \{27, 8, 1, 0\}
\]

#### C. Find the range:
The range is the set of all possible outputs (second elements) of the ordered pairs.

For Relation 1:
\[
\text{Range} = \{-3, -2, -1, 0, 1, 2, 3\}
\]

### Relation 2: \(\{(7, -3), (-5, -4), (8, 0), (0, 0), (-6, 4), (-2, 2), (-1, 3)\}\)

#### A. Determine if it is a function:
A relation is a function if each input (first element of the ordered pair) corresponds to exactly one output (second element of the ordered pair).

For Relation 2:
- Each input 7, -5, 8, 0, -6, -2, -1 corresponds to exactly one unique output.

Since each input has a unique output, Relation 2 is a **function**.

#### B. Find the domain:
The domain is the set of all possible inputs (first elements) of the ordered pairs.

For Relation 2:
\[
\text{Domain} = \{7, -5, 8, 0, -6, -2, -1\}
\]

#### C. Find the range:
The range is the set of all possible outputs (second elements) of the ordered pairs.

For Relation 2:
\[
\text{Range} = \{-3, -4, 0, 4, 2, 3\}
\]

### Summary:

**Relation 1:**
- **A.** Not a function
- **B.** Domain: \(\{27, 8, 1, 0\}\)
- **C.** Range: \(\{-3, -2, -1, 0, 1, 2, 3\}\)

**Relation 2:**
- **A.** Function
- **B.** Domain: \(\{7, -5, 8, 0, -6, -2, -1\}\)
- **C.** Range: \(\{-3, -4, 0, 4, 2, 3\}\)

Would you like any details or have any questions?

Here are 8 related questions to expand on this information:

1. What defines a function in mathematical terms?
2. How can you determine the domain of a relation?
3. How can you determine the range of a relation?
4. Can a relation be both a function and not a function? Explain.
5. How do vertical line tests help in identifying functions on a graph?
6. What are one-to-one functions and how do they differ from general functions?
7. What are the implications of having multiple outputs for a single input in a relation?
8. How do we represent functions using equations rather than sets of ordered pairs?

**Tip:** When checking if a relation is a function, ensure each input value maps to exactly one output value by verifying there are no repeated inputs with different outputs.

Explore the concepts of functions, domains, and ranges in relations through examples and explanations. Learn how to determine if a relation is a function, find its domain, and identify its range. Suitable for high school students.

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