Four functions, four corners, and one question: which one doesn’t belong? The trick is that there is no trick — every corner can be defended, so the game is never about the answer. It is about naming, precisely, the property your corner alone possesses.
| A — | B — |
| C — | D — |
A defence for every corner
- A — the only one that is increasing and has a horizontal asymptote; it doubles with every step to the right.
- B — the only one that falls and then rises, so the only one whose inverse is not a function.
- C — the only straight line, the only one through the origin, and the only one with constant first differences.
- D — the only one that decreases everywhere; each step to the right cuts it in half.
One variation
Four graphs with no equations at all — then the defences must lean entirely on the language of Transformations of Functions. Or run it in reverse: the class builds a fourth function so that a chosen corner becomes defensible.
"It looks different" scores nothing
Precision is the whole game. Not “A shoots up” but “A grows by a constant ratio while C grows by a constant amount”. That single distinction is the hinge of The Exponential Function — and deciding whether an undoing survives is the question The Inverse of a Function answers.