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:

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116