Functions and Relations

Area of Study- Functions and Graphs (unit 1)

From the VCAA 2016-2020 Mathematics Study Design

In this area of study students cover the graphical representation of simple algebraic functions (polynomial and power functions) of a single real variable and the key features of functions and their graphs such as axis intercepts, domain (including the concept of maximal, natural or implied domain), co-domain and range, stationary points, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is explored in a variety of modelling contexts and theoretical investigations.

Key skills and knowledge (outlined from the VCAA Study Design for Outcome 1)

These essentially serve a Learning Goals and Success Criteria for the topic.

• the equation of a circle with specified radius and centre
• the definition of a function, the concepts of domain, co-domain and range, notation for specification of the domain (including the concept of maximal, natural or implied domain), co-domain and range and rule of a function
• the relation between the graph of a one-to-one function, its inverse function and reflection in the line y = x
• specify the rule, domain (including maximal, natural or implied domain), co-domain, and range of a relation and identify whether or not a relation is a function
• substitute integer, simple rational and irrational numbers in exact form into expressions, including rules of functions and relations, and evaluate these by hand
• describe the effect of transformations on the graphs of relations and functions and apply matrix transformations, by hand in simple cases
• sketch by hand graphs of power functions f (x) = x^n, where n ∈ {–2, –1, (1/3) , (1/2) , 1, 2, 3, 4} and simple transformations of these, and graphs of circles

Assessment Overview

Topic tests will assess:

• key knowledge and skills,
• ability to problem-solve and use the mathematics in context,
• use of the CAS, to assist problem-solving