Non-Linear Functions
📋 What it is
Non-linear functions (quadratics curve, exponentials explode) change by different amounts each step.
🗣️ Coach says
Not all functions are straight. A quadratic (x²) curves; an exponential (2ˣ) shoots up faster and faster. Their key difference from linear: the jump between outputs KEEPS changing instead of staying constant.
🧠 Memory hook
Non-linear = the jump CHANGES each step. Curves (x²) and explosions (2ˣ), not straight lines.
😂 Giggle
What did f(x) say to g(x)?
"Let's compose ourselves!"
😲 Whoa!
A folded piece of paper doubles thickness each fold — an exponential — and just 42 folds would reach the Moon.
✅ Quick check: Outputs 1, 4, 9, 16 (the squares). Is this linear or non-linear?
Say your answer out loud first — then reveal.
Non-linear — the jumps are 3, 5, 7 (changing), not constant.
A changing rate of change means the function is not linear.
🧪 Try it! (2 minutes)
List the squares 1,4,9,16,25 and find the jumps (3,5,7,9). Notice they grow — non-linear.