IB DP A&A SL Topic 2: Functions

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.