📘 Intro to Functions – Math I

🔹 What is a Function?

• A function is a special type of relation.
  
  

• Each input (x) has exactly one output (y).
  
  

• Think of it as a machine: input → rule → output.

🔹 Relation vs. Function

• Relation = any set of ordered pairs (x, y).

• Function = each x maps to only one y.

• Example:

  • {(2, 3), (2, 5)} → ❌ Not a function
    
    

  • {(2, 3), (3, 5)} → ✅ Function

🔹 Function Notation

• Written as f(x) (read “f of x”).
  
  

• Example: If f(x) = 2x + 1, then f(4) = 2(4) + 1 = 9.

🔹 Ways to Represent a Function

• Mapping diagram → arrows show inputs to outputs

• Table of values → lists x and y

• Graph → points (x, y)

• Equation/rule → y = 3x – 2

🔹 Vertical Line Test

• A graph is a function if a vertical line touches it at only one point.

🔹 Domain & Range

• Domain = all x-values (inputs)

• Range = all y-values (outputs)

• Example: f(x) = x² for x = {–2, –1, 0, 1, 2}

  • Domain = {–2, –1, 0, 1, 2}

  • Range = {0, 1, 4}

🔹 Key Words

• Input = x (independent variable)

• Output = y or f(x) (dependent variable)

• Rule: “One input → One output = Function”