Understanding Functions in Mathematics

Definition of a Function

📌 A function assigns exactly one output to each input.
🧩 Expressed as f(x), where x is the input variable.
📊 Graphically represented as curves or lines.

Key Characteristics of Functions

🔒 Uniqueness: Every input has exactly one output.
🎯 Well-Defined: Functions follow a fixed rule.
🌐 Domain/Range: Defined set of possible inputs and outputs.

Exercises

📝 Identify the domain and range of f(x) = x² + 2.
✅ Solution: Domain = (-∞, ∞), Range = [2, ∞).
🔢 Find f(3) for the function f(x) = 2x - 5.
✅ Solution: f(3) = 2(3) - 5 = 1.
📉 Determine if the function f(x) = 1/x is defined for all real numbers.
✅ Solution: Not defined at x = 0.
📊 Graph the function f(x) = |x - 3| and describe its key features.
✅ Solution: V-shaped graph, vertex at (3,0).