Functions

Board: IB Class: AI

Chapter Overview

Modeling with linear, quadratic, exponential, and sinusoidal functions. Function transformations. Logistic growth models. Piecewise functions. Practical modeling cycle: gather data, find model, verify, predict.

Topics Covered

Linear Models
Quadratic Models
Exponential Models
Sinusoidal Models
Logistic Models
Transformations
Model Fitting

Key Formulas

y = ab^x (exponential)

y = L/(1+be^-kx) (logistic)

y = a sin(b(x-c)) + d (sinusoidal)

Real-World Applications

Applications: Population growth, disease spread, sales forecasting, temperature modeling.

Study Tips

Tip: Focus on interpreting models in context

Tip: Technology use is crucial for AI

Tip: Practice with real data sets