Types of Functions

Introduction to Functions

A function is a special relationship between values: each input value (often called x) has exactly one output value (often called y). Functions can be represented in various forms, such as equations, graphs, or tables.

In this section, we'll explore different types of functions, including one-to-one, one-to-many, and algebraic functions.

Types of Functions

• One-to-One Function: Each input has a unique output. If f(a) = f(b), then a = b.
• One-to-Many Function: Not a true function in strict mathematical terms because a single input can have multiple outputs.
• Algebraic Function: A function that can be expressed using algebraic operations (addition, subtraction, multiplication, division, and taking roots). Examples include polynomial functions, rational functions, and root functions.

Examples of Functions

• Linear Function: A function of the form f(x) = mx + c. Example: f(x) = 2x + 3.
• Quadratic Function: A function of the form f(x) = ax^2 + bx + c. Example: f(x) = x^2 - 4x + 4.
• Cubic Function: A function of the form f(x) = ax^3 + bx^2 + cx + d. Example: f(x) = x^3 - 3x^2 + 3x - 1.