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Syllabus/Passport to Advanced Math
05SAT Math

Functions & Function Notation

Functions & Function Notation

Core Concepts

  • f(x) = output when input is x
  • Domain: all valid inputs
  • Range: all possible outputs
  • Transformations

  • f(x) + k → shift up k
  • f(x) - k → shift down k
  • f(x + h) → shift left h
  • f(x - h) → shift right h
  • -f(x) → reflect over x-axis
  • f(-x) → reflect over y-axis
  • Composition

    (f ∘ g)(x) = f(g(x))
  • Work inside out: evaluate g(x) first, then apply f
  • SAT Applications

  • Evaluate f(3) given a formula or table
  • Find f(g(x)) or g(f(x))
  • Interpret function notation in word problems
  • Identify domain restrictions (no division by zero, no negative under even root)
  • Functions & Function Notation | SAT Math Prep