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Let's work through this step-by-step, focusing on the various relations, their domains, ranges, and determining whether they are functions.

### Problem 7
#### Relation:
The points shown in the graph are: (-2, 2), (0, 0), and (2, 1).

#### Domain:
The domain is the set of all x-values from the points: \{-2, 0, 2\}.

#### Range:
The range is the set of all y-values from the points: \{2, 0, 1\}.

#### Function:
A relation is a function if every x-value is mapped to exactly one y-value. Here, each x-value corresponds to a unique y-value, so **yes**, it is a function.

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### Problem 8
#### Relation:
The points shown in the graph are: (-2, -2), (0, -4), and (2, -2).

#### Domain:
The domain is the set of all x-values from the points: \{-2, 0, 2\}.

#### Range:
The range is the set of all y-values from the points: \{-2, -4\}.

#### Function:
In this case, the x-value of 2 is repeated but corresponds to the same y-value (-2), so **yes**, it is a function.

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### Problem 9
#### Relation:
The relation is given as: \{(-2, -1), (0, 3), (5, 4), (-2, 3)\}.

#### Domain:
The domain is the set of all unique x-values: \{-2, 0, 5\}.

#### Range:
The range is the set of all unique y-values: \{-1, 3, 4\}.

#### Function:
The x-value of -2 is paired with two different y-values (-1 and 3), so **no**, it is **not** a function.

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### Problem 10
#### Relation:
The relation is given as: \{(-1, 5), (0, 3), (2, 3), (3, -1)\}.

#### Domain:
The domain is the set of all unique x-values: \{-1, 0, 2, 3\}.

#### Range:
The range is the set of all unique y-values: \{5, 3, -1\}.

#### Function:
Each x-value corresponds to exactly one y-value, so **yes**, it is a function.

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Would you like further details or clarification on any of these? Here are some related questions to extend your understanding:

1. Can a relation still be a function if two points share the same y-value but different x-values?
2. How can you graphically determine if a relation is a function using the vertical line test?
3. What is the difference between a domain and a range in a relation?
4. Can a relation be both a function and not a function depending on the context or interpretation?
5. What are the different ways to express a relation: graphically, as a set of points, or as a mapping diagram?

**Tip**: Always use the vertical line test when you're unsure if a graph represents a function. If a vertical line intersects the graph more than once, it's not a function.

Express the following relations as mappings, state the domain and range, then determine if it is a function. Points are represented graphically for questions 7 and 8, and numerically for questions 9 and 10.

Learn how to express relations as mappings, determine their domains and ranges, and check if they are functions. Includes examples using graphs and ordered pairs for Grades 7-9.

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