📘Functions
🔑 What is a Function?
● A function is a rule that relates each input to exactly one output.
● Think of it like a machine: you put something in (input), the machine follows a rule, and gives exactly
one output.
Example:
f(x) = x + 2
If x = 3 → f(3) = 3 + 2 = 5
🧮 Key Terms
● Domain – the set of all possible inputs (x-values).
● Range – the set of all possible outputs (y-values).
● Function Notation – written as f(x), which means “f of x.
📊 Types of Functions
1. Linear Function: f(x) = mx + b
○ Graph is a straight line.
○ Example: f(x) = 2x + 3
2. Quadratic Function: f(x) = ax² + bx + c
○ Graph is a parabola (U-shape).
○ Example: f(x) = x² – 4
3. Cubic Function: f(x) = ax³ + bx² + cx + d
○ Graph has curves that may go up and down.
4. Absolute Value Function: f(x) = |x|
○ Graph is a V-shape.
5. Square Root Function: f(x) = √x
○ Graph starts at (0,0) and curves upward
📝 How to Check if a Relation is a Function
● Use the Vertical Line Test: If a vertical line crosses the graph more than once, it is NOT a function.
● Example: A circle is not a function, because some x-values have two different y-values.
