Functions

Board: IB Class: AA

Chapter Overview

Domain, range, and graph features. Function transformations: translations, stretches, reflections. Rational functions, asymptotes, reciprocal functions. Inverse functions (f^-1) and composite functions (fog). Quadratic functions, discriminant, sum and product of roots. Polynomial functions of higher degree.

Topics Covered

Domain and Range
Graphing Functions
Transformations
Quadratic Functions
Rational Functions
Asymptotes
Inverse Functions
Composite Functions
Polynomial Functions

Key Formulas

f(x) = a(x-h)² + k (vertex form)

x = (-b +/- √b²-4ac)/2a

f^-1(f(x)) = x

(fog)(x) = f(g(x))

Real-World Applications

Applications: Modeling projectile motion, economic cost functions, signal processing.

Study Tips

Tip: Sketch graphs for all function types

Tip: Practice domain-finding for composite functions

Tip: Use technology for verification