
Is the following relation a function? Justify your answer.

Two circles are shown, one labeled x and the other labeled y. The x circle contains the numbers 6, negative 1, 4, and 0. The y circle contains the numbers 2, negative 1, and 3. Arrows map numbers from x to numbers from y. There are arrows going from 6 to negative 1, from negative 1 to 2, from 4 to 3, and from 0 to 3.

 No, because there is an input value with more than one output value
 No, because there is an output value with more than one input value
 Yes, because each input value has only one output value
 Yes, because each output value has only one input value
Question 6 (Yes/No Worth 1 points)

The given relation can be described by the arrows mapping values from the \( x \)-circle to the \( y \)-circle. For this relation to be considered a function, each input value from \( x \) must be associated with **only one** output value from \( y \).

Here’s the breakdown of the mapping:
- \( 6 \) maps to \( -1 \)
- \( -1 \) maps to \( 2 \)
- \( 4 \) maps to \( 3 \)
- \( 0 \) maps to \( 3 \)

In this case, **each input value from the set \( x \)** (6, -1, 4, 0) is associated with exactly one output value in \( y \). There is no input that maps to more than one output, which satisfies the definition of a function.

### Conclusion:
The relation **is** a function because each input has only one output.

So, the correct justification is:
- **Yes, because each input value has only one output value.**

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Would you like more details or have any other questions?

Here are 5 related questions for further exploration:
1. What is the formal definition of a function in mathematics?
2. Can a function have more than one input value mapping to the same output value?
3. What is the difference between a relation and a function?
4. How can we represent a function using a graph?
5. What happens if an input value is mapped to two different output values?

**Tip:** Always remember, for a relation to be a function, each input must correspond to only one output.

Is the following relation a function? Justify your answer.

Two circles are shown, one labeled x and the other labeled y. The x circle contains the numbers 6, negative 1, 4, and 0. The y circle contains the numbers 2, negative 1, and 3. Arrows map numbers from x to numbers from y. There are arrows going from 6 to negative 1, from negative 1 to 2, from 4 to 3, and from 0 to 3.

Learn how to determine if a relation is a function by analyzing the mappings between two sets. This problem explores key concepts in functions and relations and is suitable for students in Grades 6-8.

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