# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Function mapping: deciding whether a rule is a function, and separating codomain, range and graph](/en/derivations/derivation-mko-function-mapping-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-function-mapping)

Let X={−2,−1,0,1,2}, Y={0,1,2,3,4,5} and f:X→Y, f(x)=x². Prove that f is a function; compute the range f(X)={0,1,4} and show f(X)≠Y; write down the graph Γ_f; and show that changing the codomain to {0,1,4} gives a different function. Then decide two non-examples: the reverse rule s(y)='the x in X with x²=y' is not a function Y→X, and g(x)=x+4 is not a function X→Y.

Function mapping

derivation-mko-function-mapping-01





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