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Functions: notation, domain, range and the vertical line test

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Useful for: MCR3U MCF3M IB Math AA SL & HL IB Math AI SL & HL AP® Precalculus

Learn it A relation is a function if every input (x) has exactly one output (y): on a graph, no vertical line crosses it twice. The domain is the set of allowed x-values; the range is the set of y-values the function actually produces.

Example: State the domain and range of f(x) = √(x − 3) + 2.

  1. Inside the root must be ≥ 0: x − 3 ≥ 0, so the domain is x ≥ 3.
  2. √(x − 3) is at least 0, so f(x) is at least 2: the range is y ≥ 2.

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