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To determine if the given relation is a function, we need to examine whether each input (or "x-value") corresponds to only one output (or "y-value").

The relation provided is:

\[
(4, 2), (2, -1), (0, -4), (2, -7), (4, -10)
\]

A relation is a function if no two ordered pairs have the same first element (x-value) paired with different second elements (y-values). Let's check the x-values:

- \( 4 \to 2 \)
- \( 2 \to -1 \)
- \( 0 \to -4 \)
- \( 2 \to -7 \) (Note: this is the same x-value, 2, but with a different y-value, -7)
- \( 4 \to -10 \) (Again, the same x-value, 4, but with a different y-value, -10)

Since both 2 and 4 are mapped to multiple different y-values, this violates the condition for being a function. Therefore, **this relation is not a function**.

Would you like further clarification on this concept or more examples?

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Here are 5 related questions to deepen your understanding:

1. What is the definition of a function in terms of ordered pairs?
2. How do we graphically determine whether a relation is a function?
3. What happens if a relation has the same y-value for different x-values?
4. Can a relation be a function if two ordered pairs have the same x and y-values?
5. How does the vertical line test help determine if a graph represents a function?

**Tip**: When verifying if a relation is a function, always check for repeated x-values with different y-values!

Determine whether the relation (4, 2), (2, -1), (0, -4), (2, -7), (4, -10) is a function.

Determine if the given relation (4, 2), (2, -1), (0, -4), (2, -7), (4, -10) is a function by examining repeated x-values and their corresponding y-values. Suitable for Grades 7-10.

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