Misconceptions & Reasoning
📋 What it is
Common traps: assuming every pattern is linear, confusing input and output, mis-reading a graph.
🗣️ Coach says
Knowing the traps makes you sharp. Not every pattern is a straight line. Don't swap input and output. A graph going up doesn't always mean "adding" — it could be a curve. Naming a trap stops you falling in.
🧠 Memory hook
Not every pattern is linear. Keep input and output straight. Read the graph's SHAPE, not just "up".
😂 Giggle
Why couldn't the vertical line be a function?
Because it failed the vertical line test — it gave two outputs for one input!
😲 Whoa!
A classic error: assuming a pattern that starts 2, 4… must be "×2" — but it could be "+2" (giving 6, not 8). Always check a third term.
✅ Quick check: A pattern starts 2, 4. Is the rule definitely "double it"?
Say your answer out loud first — then reveal.
No — it could be "+2" (→6) or "×2" (→8). You need a third term to tell.
Two points fit many rules; a third distinguishes them.
🪄 Trick question: In a function, can one input give two different outputs?
Careful — think it through, then reveal.
No — a function gives exactly ONE output per input.
Two outputs for one input breaks the definition of a function.
🧪 Try it! (2 minutes)
Show 3, 6 and ask a friend the rule. It could be +3 or ×2 — prove it with the next term.