Pure mathematicians may hate this idea, but for Algebra students I explain the notation f(x) as just y in disguise. My friend, Joy, took this idea a step further and shared this with me:

A note of thanks for the f(x) being “y in disguise.” I introduced it today wearing two masks (one hidden underneath). Told them I was planning to go out on Halloween as the “mean green function machine” (masks are green, one of our school colors). The top mask I wrote on it f(x) and the one underneath was, of course, y. So when I said you only need to remember f(x) is y in disguise, I whipped off the top mask and they saw the y underneath. It was great! And for a Friday, especially my 6th period, it woke them up and they had a blast! And so did I!