I'm teaching a College Algebra class in the upcoming semester, and only a small portion of the students will be moving on to further mathematics. The class is built around functions, so I need to start with the definition of one, yet many "official" definitions I have found too convoluted (or poorly written) for general use.
Here's one of the better "light" definitions I've found:
A function is a relationship which assigns to each input (or domain) value, a unique output (or range) value."
This sounds simple enough on the surface, but putting myself "in the head" of a student makes me pause. It's almost too compact with potentially ambiguous words for the student (relationship? assigns? unique?)
Here's my personal best attempt, in 3 parts. Each part of the definition would include a discussion and examples before moving to the next part.
A relation is a set of links between two sets.
Each link of a relation has an input (in the starting set) and an output (in the ending set).
A function is a relation where every input has one and only one possible output.
I'm somewhat happier here: starting with a relation gives some natural examples and makes it easier to impart the special importance of a function (which is "better behaved" than a relation in practical circusmtances).
But I'm also still uneasy ("links"? A set between sets?) and I was wanting to see if anyone had a better solution.