From the IB:IB DP A&A SL Topic 2: Functions IB Essential understandings:Models are depictions of real-life events using expressions, equations or graphs while a function is defined as a relation or expression involving one or more variable. Creating different representations of functions to model the relationships between variables, visually and symbolically as graphs, equations and/or tables represents different ways to communicate mathematical ideas. Content-specific conceptual understandings: • Different representations of functions, symbolically and visually as graphs, equations and tables provide different ways to communicate mathematical relationships. • The parameters in a function or equation may correspond to notable geometrical features of a graph and can represent physical quantities in spatial dimensions. • Moving between different forms to represent functions allows for deeper understanding and provides different approaches to problem solving. • Our spatial frame of reference affects the visible part of a function and by changing this “window” can show more or less of the function to best suit our needs. • Changing the parameters of a trigonometric function changes the position, orientation and shape of the corresponding graph. • Different representations facilitate modelling and interpretation of physical, social, economic and mathematical phenomena, which support solving real-life problems. • Technology plays a key role in allowing humans to represent the real world as a model and to quantify the appropriateness of the model. Syllabus: |