Concept guide
Mathematical representation: deciding whether words, a formula, tables and ordered pairs represent the same function
Fix the object f:D→ℤ with D={0,1,2,3} and f(x)=2x−1. Decide: the words 'double the input, then subtract 1' correspond to 2x−1; the table T1={(0,−1),(1,1),(2,3),(3,5)} represents f; the set of ordered pairs is the graph of f; the affine rule is recovered uniquely from the two rows (1,1) and (3,5); the table T2, with (3,5) replaced by (3,6), represents neither f nor any affine rule; T3, with a repeated input, is not a function table; g(x)=2x−1 defined on ℤ is not the same function as f; and a table supplies no values at unlisted points.