Critical Analysis & Evaluation
📋 What it is
Judge whether a claimed rule fits the data; find the error in a function.
🗣️ Coach says
Not every proposed rule is right. Test it against the table: if the rule gives the wrong output for even one input, it's wrong. Checking a function against its data catches most mistakes.
🧠 Memory hook
Test the rule on EVERY row. One wrong output means the rule is wrong.
😂 Giggle
Why was the quadratic function always smiling?
Because it was always positive — at least at its vertex!
😲 Whoa!
Scientists reject a formula the moment it fails to predict even one careful measurement — one miss is enough.
✅ Quick check: Someone says the rule for 1→3, 2→5, 3→7 is "×3". Check it — is it right?
Say your answer out loud first — then reveal.
No: ×3 gives 3,6,9 not 3,5,7. The rule is 2x + 1.
Testing the rule against every pair exposes the error.
🧪 Try it! (2 minutes)
Given inputs 1,2,3 → outputs 5,7,9, test the guess "×5". Does it fit? Find the real rule (2x+3).