Question

Devon is having difficulty determining if the relation given in an input-output table is a function. Marco explains to him that in order to tell if the relation in the table is a function, Devon needs to check if any of the output values are repeated. If they repeat and have different input values, the relation is not a function.

Summarize Marco's reasoning in your own words.

a) Marco is correct; a function has unique output values for each input.

b) Marco is incorrect; the repetition of output values does not affect the function.

c) Marco is correct only if there are no repeated input values.

d) Marco is incorrect; a function can have repeated output values for different inputs.

Answer 1

Marco's reasoning is partially correct; a relation where inputs have unique outputs is a function, but repeating output values do not define whether a relation is a function or not.

Step-by-step explanation:

Marco's explanation about how to determine if the relation in an input-output table is a function can be summarized as follows: In mathematics, a function is defined as a relation where each input is associated with a unique output. This means that even though an output value can repeat, what is crucial is that each input value is paired with one output value only. If an input has multiple different outputs, then the relation is not a function. Therefore, Marco's assertion is partially correct, but his focus on repeated output values is misleading. Instead, Devon should check for inputs having multiple different outputs to determine if the relation is not a function. The correct reasoning is aligned with option (d) where Marco is incorrect; a function can indeed have repeated output values for different inputs.