Algebra 1

Algebra 1 introduces students to the fundamental concepts of algebra, including variables, equations, and functions.

Basic Concepts

Functions and Their Graphs

What Is a Function?

A function is a special rule that takes an input, does something to it, and gives back an output. Think of it like a vending machine: you put in money (input), and you get a snack (output).

How Do Functions Work?

Functions are often written as \( f(x) \), which means “the function of \( x \).” If \( f(x) = x + 2 \), and you plug in \( x = 3 \), you get \( f(3) = 3 + 2 = 5 \).

Graphing Functions

You can draw a picture of a function using a graph. Each input-output pair becomes a point on a graph, and connecting these points shows the pattern.

Why Are Functions Useful?

Functions help us model everything from how fast you run to how much money you save. They are everywhere in science and technology!

Examples

  • If \( f(x) = 2x \), then \( f(4) = 8 \).

  • The graph of \( y = x + 1 \) is a straight line going up.

In a Nutshell

Functions link each input to exactly one output and can be shown on a graph.