https://file.aiquickdraw.com/mathbot/file/1726908077693af37puqk.jpg

In the image provided, we have several ordered pairs representing relations, and there are two tasks:

1. **Graphing the relations:**
   - For relations 3 and 4, the ordered pairs are to be graphed on the coordinate plane provided.

2. **Representing the relations as mapping diagrams:**
   - For relations 5 and 6, the ordered pairs are to be shown in a mapping diagram, where each domain (x-values) is mapped to its corresponding range (y-values).

### Let's start by graphing the points for relations 3 and 4:

#### **Relation 3:**
Set of ordered pairs: \(\{(-3, -6), (-1, 6), (0, 4), (5, 3), (7, 1)\}\)

- Plot the following points on the left graph:
  - \((-3, -6)\)
  - \((-1, 6)\)
  - \((0, 4)\)
  - \((5, 3)\)
  - \((7, 1)\)

#### **Relation 4:**
Set of ordered pairs: \(\{(-2, 7), (0, 1), (3, -7), (7, -2), (7, 0)\}\)

- Plot the following points on the right graph:
  - \((-2, 7)\)
  - \((0, 1)\)
  - \((3, -7)\)
  - \((7, -2)\)
  - \((7, 0)\)

### Now for the mapping diagrams for relations 5 and 6:

#### **Relation 5:**
Set of ordered pairs: \(\{(-6, -7), (-6, 3), (0, -7), (3, -4), (5, 6)\}\)

- In a mapping diagram, write the domain (x-values) on the left and the range (y-values) on the right:
  - Domain: \(\{-6, 0, 3, 5\}\)
  - Range: \(\{-7, 3, -4, 6\}\)
- Draw arrows mapping:
  - \(-6 \rightarrow -7\) and \(-6 \rightarrow 3\)
  - \(0 \rightarrow -7\)
  - \(3 \rightarrow -4\)
  - \(5 \rightarrow 6\)

#### **Relation 6:**
Set of ordered pairs: \(\{(-6, 7), (-5, 6), (3, 5), (3, -4), (6, 4)\}\)

- Domain: \(\{-6, -5, 3, 6\}\)
- Range: \(\{7, 6, 5, -4, 4\}\)
- Map:
  - \(-6 \rightarrow 7\)
  - \(-5 \rightarrow 6\)
  - \(3 \rightarrow 5\) and \(3 \rightarrow -4\)
  - \(6 \rightarrow 4\)

Let me know if you'd like me to graph these relations for you, or if you have any questions!

Here are 5 related questions to deepen your understanding:
1. What defines a relation in mathematics?
2. How can you determine if a relation is a function from a graph?
3. How does a mapping diagram visually represent a relation?
4. What does it mean for a point to be an outlier in a graph of relations?
5. How do ordered pairs relate to the concept of a function?

**Tip:** Remember, a relation is a function if each input (x-value) has exactly one output (y-value).

Each set of ordered pairs represents a relation. Represent the relation as a graph or mapping diagram.

Learn how to represent relations through graphing ordered pairs and mapping diagrams. This problem involves graphing points on a Cartesian plane and using mapping diagrams to connect domains and ranges, suitable for students in Grades 6-8.

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