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.