Variables

Definition

Variables are symbols (usually letters) that represent values that can change or are unknown within a given mathematical expression or programming context.

Why It Matters

Variables are the foundation of abstraction. They allow us to write general formulas, express functional relationships, and write software programs that run with dynamic data.

Core Concepts

• Dependent vs. Independent: In $y = f(x)$, $x$ is the independent variable (input) and $y$ is the dependent variable (output).
  • How to read: “y equals f of x.”
  • Meaning: y is a function of x, where x determines the value of y.
• Scope in Programming: Variables in code have scope (local vs global) indicating where they can be accessed.

Connected Concepts

• Constants
• Function Definition, Function Notation