Function notation, terminology and quadratic functions
Overall Expectations
Understand the definition of a function, including function notation, algebraic, mapping and graphical representations Understand features of functions including domain/range Understand, analyse and apply various families of functions, including polynomial and square root functions Understand and apply composite and inverse functions
Conceptual Framework
relationships change model representation in the context of Scientific & Technical Innovation
Statements of Inquiry
Understanding of functional relationships enable us to manipulate and apply functions in a range of contexts
Factual
What defines a mathematical function?
Conceptual
How can we use functions to better understand change?
Debatable
Is an inverse function truly an inverse function?
Description
The focus of this unit will be on mathematical functions, their representation and application to model change, with a particular emphasis on quadratic functions. Students will be introduced to the concept of mathematical functions and the various ways they can be represented. Students will work with functions numerically, algebraically and graphically, identifying any restrictions. Students will apply their knowledge of functions to model linear and quadratic relationships. Students will also apply the mathematical concept of an inverse to functions, with a particular focus on graphical analysis. The unit will conclude with students investigating functional transformations, linking the changes in algebraic form to the graphical form.
Learning Outcomes
Define a function as having only one output for any given input
Define domain and range
Map functions from the domain to range
Understand and use proper function notation
Evaluate and manipulate functions
Evaluate and manipulate composite functions
Review and interpret graphs of linear functions
Determine the inverse of a linear function
Represent functions and their inverses graphically
Factorize, manipulate, solve and graph quadratic functions
Understand the square root function as the inverse of a quadratic function
Solve and express inverse functions graphically, by mapping and by solving equations
Use the GDC to graph and analyse other functions (such as higher order polynomials, absolute value)
Identify the characteristics of a variety of polynomial functions, including domain, range, maximum, minimum values