How would you explain function notation to a friend?

Many students seem puzzled by function notation well after it has been introduced, and ask “why can’t we just write

y = 3x instead of

f(x) = 3x ?”. To motivate the use of function notation and improve understanding, I advocate using multi-variable functions instead of single-variable functions in introducing this notation. My introduction usually proceeds something like this:

Step-by-step explanation:

step-by-step explanation: