Question 13

A table showing a function is represented by option A.

A function is defined as a relationship where each input corresponds to exactly one output. The table in option A demonstrates this characteristic by ensuring that each value in the input column maps to a unique value in the output column.

A) m-43a.png

This table accurately represents a function because for every input value, there is exactly one corresponding output value. No input value is repeated, confirming that it meets the definition of a function.

B) m-43b.png

This table does not represent a function as it contains multiple output values for at least one input value. The presence of repeated input values with different outputs violates the fundamental definition of a function.

C) m-43c.png

Similar to option B, this table fails to show a function because it features an input value that corresponds to more than one output value. This inconsistency disqualifies it as a valid function.

D) m-43d.png

This table does not illustrate a function either, as it also contains repeated input values linked to different outputs. This means that it does not adhere to the rule that each input must correspond to a single output.

Conclusion

Option A is definitively the correct choice because it adheres to the definition of a function by ensuring that each input is associated with a unique output. In contrast, options B, C, and D each demonstrate instances where inputs are linked to multiple outputs, thus failing to qualify as functions.