My Exam Guide

Effervescence Simulation

Interactive Function Visualizer 🎯 Interactive Function Visualizer Identity: f(x) = x Square: f(x) = x² Cube: f(x) = x³ Modulus: f(x) = |x| Signum: f(x) = sign(x) Step: f(x) = ⌊x⌋ Exponential: f(x) = e^(x/4) Logarithmic: f(x) = log(x)

Types of Functions Types of Functions in Mathematics Definition: A function is a relation where each input has exactly one output. 1. Based on Mapping Type Description Example One-One (Injective) Each input maps to a unique output f(x) = 2x + 1 Onto (Surjective) Every output has a pre-image in the domain f(x) = x³ (if domain = codomain = ℝ) Bijective Both injective and surjective f(x) = x + 5 Many-One Multiple inputs have the same output f(x) = x² 2. Based on Expressions Type Description Example Algebraic Function Uses algebraic expressions f(x) = 3x² + 2x + 1 Polynomial Function Polynomial of x f(x) = x³ - 2x + 5 Rational Function Ratio of two polynomials f(x) = (x² + 1)/(x - 3) Irrational Function Involves roots f(x) = √(x + 4) 3. Based on Values Type Description Example Constant Function Always gives same output f(x) = 7 Identity Function Output equals input f(x) =...