At a school, is a student's ID number a function of their last name? Assume there are students with the same last name.

Yes, because every student has a last name and an ID number.

No, because a single last name (input) could correspond to multiple different ID numbers (outputs).

Yes, because each student has a unique ID number.

No, because some last names are longer than others.

Consider the relation $T = \{(\text{apple}, \text{red}), (\text{banana}, \text{yellow}), (\text{grape}, \text{red})\}$. Is this relation a function?

Yes, because each input (fruit) has exactly one output (color).

No, because the output 'red' is paired with two different inputs.