A function is a machine.  You put something in it and something else comes out.  A function has a set of rules that tells you what to do once you put something in it.

f(x) is read as “f of x” — not “f times x”. This means the function’s name is “f” and “x” is what goes in it.

Example:

f(x) =3x – 5

When you put x into the function, f, above… the function will multiple it by 3 and then subtract 5.

f(4) = 3*4 – 5 = 12 – 5 = 7

f(0) = 3*0 – 5 = 0 – 5 = -5

You can even put other letters in the function:

f(y) = 3*y – 5 = 3y – 5 (cannot simplify more than that!)

Whatever I put in the function just simply replaces the original “x”:

f(6-x) = 3(6-x) – 5 = 18 – 3x – 5 = 13 – 3x.

Let’s consider a new function now:

f(x) = x² – 5x + 7

So,

f(0) = 0² – 5(0) + 7 = 0 – 0 + 7 = 7.

Notice that the 0 replaced each x?

Here is a mini quiz.  Leave your answers as comments to see if you are understanding functions:

If f(x) = x² -5x + 7

1.  What does f(4) = ?

2.  What does f(p) = ?

3.  What does f(7-y) = ?