Math 1 · Unit 2 · Lesson 1 · part 3 of 8

The notation f(x), read f of x

Mathematicians write a function with a letter and parentheses: f(x) .

The notation f(x), read f of x

Mathematicians write a function with a letter and parentheses: f(x). Read it out loud as f of x. It means a function of x: a rule that x feeds into. The parentheses here are not multiplication. They are the slot the input goes into.

When we write f(x) = x + 3, we are saying two things at once: the formula is x + 3, and x is the number that is going to feed into it. The spreadsheet version is B1 = A1 + 3, where A1 plays the part of x.

To use the function, put a number in the slot. f(4) means feed in 4, so replace every x in the formula with 4: f(4) = 4 + 3 = 7. The 4 is the input, the 7 is the output.

f(x) = x + 3

f(4) = 4 + 3 = 7

f(0) = 0 + 3 = 3

f(−5) = −5 + 3 = −2

g(x) = 2x

g(3) = 2 × 3 = 6

g(−1) = 2 × (−1) = −2

g(12) = 2 × 12 = 1

h(x) = 3x − 1

h(2) = 3 × 2 − 1 = 5

h(0) = 3 × 0 − 1 = −1

h(−2) = 3 × (−2) − 1 = −7

k(x) = x × x

k(3) = 3 × 3 = 9

k(−3) = (−3) × (−3) = 9

Two inputs can share an output. That is fine. One input can never have two outputs.

Any letter can name a function: f, g, h, k, or even a whole word. The letter just tells the functions apart when there is more than one, the way A1 and B1 tell cells apart.

Sometimes we write y instead of f(x). The output has two names. In higher math, like calculus, it is almost always written f(x). When you are learning to graph, it is almost always written y. So y = x + 3 and f(x) = x + 3 are the same rule, and a table of x and y is the same as a table of x and f(x). This lesson uses both on purpose, so you get used to both.

Where to go next

Next: The coordinate plane, and how to plot a pointTake two number lines and cross them at zero. All the partsWhat a Function Is: One In, One Out