Lesson 4.7

Function Notation

It looks like multiplication, but it's not. It's just a nametag. Meet , the most famous symbol in algebra.

Introduction

Until now, we've used . But what if we have two different equations? Calling them both "y" gets confusing. So we give them names. We call the first one (for function) and write .

Past Knowledge

Lesson 4.1 (Equations visually). Understanding that input leads to output.

Today's Goal

Read, write, and understand the symbol . Realize that is just a fancy way to write .

Future Success

This notation is mandatory for Calculus (, ). You must master it now.

Key Concepts

Anatomy of a Function

f(x)

The Name. Just like "Fred" or "Frank". It tells us WHICH machine we are using.

The Input. This is what we are feeding into the machine.

The Output (y). The entire symbol represents the Result, or the y-value.

Read it as: "f of x"

Worked Examples

Example 1: Translating to Points

Basic

If , what is the ordered pair?

Identify Parts

The number INSIDE the parentheses is Input (x). .

The number on the other side is Output (y). .

(3, 10)

Example 2: Reading a Graph

Intermediate

A graph passes through the point . Write this using function notation.

Format: f(Input) = Output

Input is . Output is .

f(5) = -2

Example 3: Comparing Function Values

Advanced

If and , which function is larger at ?

Compare Outputs

At input 2, Function f outputs 5. At input 2, Function g outputs 8.

Since , is larger.

g(2) > f(2)

Common Pitfalls

It is NOT Multiplication

does NOT mean . You cannot divide by . The parentheses here mean "holding", not "multiplying".

The Empty F

You can't just write . A function needs an input. It must be . Just like you can't have a "square root" symbol floating without a number inside it.

Real-Life Applications

Code: In programming, function notation is literal. calculateTax(price). Determining the tax of the price. If you wrote calculateTax * price, the computer would crash. Algebra is the original coding language.