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.