Questions: Does the following table of input/output information represent a function? Input Output shirt red jacket yellow pants green shoes purple socks orange shirt black No, because the same input has two different outputs. Yes, because for each output there is only one input. Yes, because for each input there is only one output. No, because for each output there is only one input.

Solution Steps

To determine if the table represents a function, we need to check if each input maps to exactly one output. If any input maps to more than one output, it is not a function.

We have the following input-output pairs from the table:

• \( \text{shirt} \rightarrow \text{red} \)
• \( \text{jacket} \rightarrow \text{yellow} \)
• \( \text{pants} \rightarrow \text{green} \)
• \( \text{shoes} \rightarrow \text{purple} \)
• \( \text{socks} \rightarrow \text{orange} \)
• \( \text{shirt} \rightarrow \text{black} \)

A relation is a function if each input corresponds to exactly one output. In this case, the input \( \text{shirt} \) maps to two different outputs: \( \text{red} \) and \( \text{black} \). This violates the definition of a function.

Since the input \( \text{shirt} \) has two different outputs, we conclude that the relation does not represent a function.

Final Answer