Form and Function

Mathematics deals with abstract objects, and relations between them. In school, these correspond with sets, represented by domain, range and variables; equations, inequalities and functions. Even geometry may be described in these general terms. Such a generalized description of mathematics is centred on this fundamental concept, function.

In this course, we shall explore the definition and role of function, including relations, beyond just drawing and interpretation of graphs. Examples will include the usual tables of values (coordinate pairs), equations, graphs and inverses (Grade 12), but will also extend to sequences, symmetry and transformations; even infinity!

The learning outcomes with reference to CAPS and Grade 11 (R)ATP, 2024 are specified in the Sessions below.

In general, across all sessions, the following characteristics and features of functions and graphs will necessarily be present:

• domain and range; intercepts with the axes; turning points; minima, maxima; asymptotes (horizontal and vertical); shape and symmetry; average gradient (average rate of change); intervals on which the function increases or decreases.

Session 1 - 18 April (15h30 - 17h30)

We shall

• Examine general definitions and concepts of Relations and Functions, and Inverses (Grade 12).
• Revise representations of function as abstract diagrams of domains and codomains (range), tables of values, graphs, equations, and other forms of description.
• Interpret equations as intersection of functions; and inequalities as relations involving linear and quadratic expressions as initial examples.
• Revise and explore the effect of the parameters  and  on the functions and graphs defined by

• y = f(x) = ax² + q.
• y = f(x) = a/x + q.
• y = f(x) = ab^x + q, where b > 0,b = 1.

• Include: Clarifying examples, exercises, questions, problems.
• Use GeoGebra for illustration, demonstration and verification purposes.

The course/session will make specific reference to the ATPs, and classroom strategies or issues involved in the teaching-learning of the content/concepts.

Session 2 - 25 April 2024 (15h30 - 17h30)

We shall

• Investigate and explore the effect of the parameters ,  and  on the functions and graphs defined by
  
  • y = f(x) =a(x + p)² + q.
  • y = f(x) = 2/x+p + q.
  • y = f(x) = ab^x+p + q, where b > 0, b = 1.
• Include: Clarifying examples, exercises, questions, problems.
• Use GeoGebra for illustration, demonstration and verification purposes.
• NCS Exam questions

The course/session will make specific reference to the ATPs and classroom strategies and issues involved in teaching-learning of the content/concepts.

Session 3 - 9 May 2024 (15h30 - 17h30)

We shall

• Investigate and explore the effect of the parameters ,  and  on the functions and graphs. 

[as per CAPS, for at most two parameters at a time].

• Inverses: some examples and the concept across the algebraic and trigonometric functions. Even though inverses are assigned to Grade 12, the elementary concept will be introduced for linking Grade 11 with Grade 12, and for completeness.
• Include: Clarifying examples, exercises, questions, problems.
• Use GeoGebra for illustration, demonstration and verification purposes.
• NCS Exam questions

The course/session will make specific reference to the ATPs and classroom strategies and issues involved in teaching-learning of the content/concepts.