To supplement my graduate student income, I have been tutoring in my department for several years. Many know how to manipulate them, but have never actually considered…
What is a function?
Metaphor allows us to explain that which is novel with that which is familiar.
Imagine you have a blender. If you put in ingredients for a smoothie, you better get a smoothie out. If pancake batter magically appeared instead, you’d either be elated (because, pancakes), or really really upset.
Getting the same output for a given input is what defines a function.
There are lots of ways to make a smoothie. It’s fine for different inputs to lead to the same output. As long as the same inputs don’t result in different outputs, you have a function.
Only one possible output can come from each viable input.
(this is what your instructor might have called “the vertical line test”)
