Which table shows a function?

Rationale

Table A) m-43a.png shows a function.

A function is defined as a relation where each input (or x-value) corresponds to exactly one output (or y-value). Table A meets this criterion, as it pairs each unique input with a single output, demonstrating the fundamental property of a function.

A (m-43a.png) CORRECT

This table presents a clear mapping of inputs to outputs, where no input value is repeated, ensuring that each x-value corresponds to one and only one y-value. As such, it qualifies as a function by the definition of mathematical relations.

B (m-43b.png) YOUR ANSWER

In this table, at least one input value is associated with multiple output values. This violates the definition of a function, as a function cannot have more than one output for a single input. Therefore, it does not represent a function.

C (m-43c.png) YOUR ANSWER

This table also exhibits multiple outputs for the same input, indicating that one x-value corresponds to more than one y-value. This characteristic disqualifies it from being classified as a function since it fails to meet the unique output requirement.

D (m-43d.png) YOUR ANSWER

Similarly, this table contains instances where an input is linked to multiple outputs, which is inconsistent with the definition of a function. The presence of multiple y-values for a single x-value indicates that this table does not represent a function.

Conclusion

To summarize, a function must assign exactly one output to each input. Among the options provided, only table A) m-43a.png adheres to this principle, making it the only valid representation of a function. The other tables exhibit violations of the fundamental definition of a function, demonstrating that understanding these relationships is crucial in distinguishing valid functions from non-functions in mathematical contexts.

Which table shows a function?

Table A) m-43a.png shows a function.

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