Function Notation and Transformations

SAT Math · Axiom Academy

Function Notation & Transformations Master f(x), Composition, and Graph Shifts Understanding Function Notation Function notation is a compact way to express "y in terms of x." NOT f times x—it means "apply the function to x" Can easily show different functions: f(x), g(x), h(x) Makes composition and operations clear Shows input-output relationship explicitly Composition means plugging one function into another. Then: Use that result as input to f Important: Composition Order Matters! Composition is NOT commutative. Order counts! How does changing the function formula affect its graph? Four Types of Transformations: Critical Trap: Horizontal Shifts NOT left! The negative is inside, so it flips direction. Think: "To get the same output, x must be 3 larger" Example: Describe Transformations Stretch vertically by 2 (2× coefficient) You can add, subtract, multiply, and divide functions just like numbers. Composition f(g(x)) is much more common than operations. Master that first!

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