Summary of the Rules

Transformations of any family of functions follow these rules:

  • f(x) + c is f(x) translated upward c units
  • f(x) - c is f(x) translated downward c units
  • f(x + b) is f(x) translated left b units
  • f(x - b) is f(x) translated right b units
  • -f(x) is f(x) reflected about the x-axis
  • f(-x) is f(x) reflected about the y-axis
  • a•f(x) stretches the graph vertically if a > 1
  • a•f(x) shrinks the graph vertically if 0 < a < 1
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