https://file.aiquickdraw.com/mathbot/file/1728170134769zeukvrsu.jpg

Let's analyze the relation shown in the image.

### Points in the relation:
The graph contains four points:
- \((-2, 3)\)
- \((1, 5)\)
- \((1, 2)\)
- \((4, -1)\)

### Domain and Range:
- **Domain**: The domain consists of the \(x\)-coordinates of all the points. From the graph:
  \[
  D = \{-2, 1, 4\}
  \]
  Note: \(1\) appears twice in the list of points, but we only include it once in the domain.
  
- **Range**: The range consists of the \(y\)-coordinates of all the points. From the graph:
  \[
  R = \{3, 5, 2, -1\}
  \]

### Determining if it's a function:
For a relation to be a function, each input (or \(x\)-coordinate) must correspond to exactly one output (or \(y\)-coordinate). In this relation, the \(x\)-value \(1\) is paired with both \(5\) and \(2\). Since one \(x\)-value is paired with multiple \(y\)-values, **this is not a function**.

### Type of relation:
This relation is **not a function** because one input corresponds to multiple outputs.

Would you like further details or clarifications? Here are 5 related questions you might explore:

1. What is the difference between a function and a general relation?
2. How can you graphically determine if a relation is a function using the vertical line test?
3. Can a relation have repeating \(y\)-values and still be a function?
4. How are domain and range different in continuous versus discrete relations?
5. How does the concept of a one-to-one function differ from a general function?

**Tip**: To determine if a relation is a function, check if any \(x\)-value is paired with more than one \(y\)-value. If it is, the relation is not a function.

State the domain and range of this relation. Then determine if it is a function or not a function.

Learn how to determine the domain and range of a relation from a graph and assess whether the relation represents a function. This problem includes key algebraic concepts related to relations and functions, suitable for high school students in Grades 9-12.

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