Properties of Functions

Pure Mathematics — Second Secondary

Common mistakes

Comparison aspect	Main idea	Keywords
Confusing even with odd	even means f(−x) = f(x) while odd means f(−x) = −f(x)	meanswhile
Wrong substitution of a negative number	(−2)² = 4 but −2² = −4. Always write brackets when substituting −x	Alwayswritebracketssubstituting
Judging a property from one point	checking one value of x does not prove evenness or oddness. To prove a property you must check it for all x and to disprove it one counterexample is enough	checkingvaluedoesprove
Forgetting the symmetric domain	a function whose domain is not symmetric about zero cannot be even or odd	functionwhosezerocannot

Properties of Functions · 4 / 5