ConceptFunctions & Sequences
← All conceptsMonotonicity and parity
7 ways this goes wrong. Each one is a named misconception the questions are built to catch.
- Composite monotonicity mis-combinedCombines inner and outer monotonic behaviors incorrectly for a composite function.→
- Constant term breaks symmetryMisapplies the symmetry test to a function with a constant term that destroys oddness.→
- Even called oddLabels an even function odd (or neither) by misapplying f(-x)=-f(x).→
- Increasing/decreasing sign flippedConfuses where f'(x)>0 with where f'(x)<0, reversing monotonic direction.→
- Parity domain symmetry ignoredDeclares parity without checking the domain is symmetric about 0.→
- Quadratic vertex vs intervalIgnores where a quadratic's vertex sits relative to the queried interval.→
- Shift not accounted in parityConcludes f is odd/even without accounting for an additive shift (e.g. f(x)+1 is odd, not f).→
