From the IB

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.