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Parent functions and their key features

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

Learn it Know the shapes of the parent functions: y = x (line), y = x² (parabola), y = x³ (S-curve), y = √x (half-parabola from the origin), y = 1/x (hyperbola with asymptotes x = 0 and y = 0), y = |x| (V shape). Each has a typical domain and range.

Example: Which parent function has domain x ≥ 0 and range y ≥ 0?

  1. y = x² has domain all real numbers, so not that one.
  2. y = √x: inputs must be ≥ 0 and outputs are ≥ 0.

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