- Mathematical Methods
- Year 11
Functions and Graphs
approx. 14 hrs
5 topics
32 concepts
Build mastery in Functions and Graphs to demonstrate proficiency in assessment and examination tasks.
approx. 14 hrs
5 topics
32 concepts
Build mastery in Functions and Graphs to demonstrate proficiency in assessment and examination tasks.
In this learning program, students explore the graphical representation of simple algebraic functions including polynomials and power functions of a single real variable. We will equip students with the knowledge and skills required to work effectively with functions and graphs. This will involve a thorough investigation into 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. Students will study the behaviour of functions and their graphs in a variety of modelling contexts and theoretical investigations.
This learning program is made up of the following 5 topics, broken down into 32 concepts.
Writing and interpreting interval notation
Writing and interpreting the empty set
Writing and interpreting elements of a set
Writing and interpreting intersection of more than one set
Writing and interpreting sets of numbers
Writing and interpreting set difference
Writing and interpreting subsets
Writing and interpreting the union of more than one set
Writing and interpreting infinite sets
Determine if a function is one-to-one
Even and odd functions
Use function notation to find the output of a single function
Use the vertical line test on a graph to decide whether it represents a function
Finding the output of a piecewise defined function
Identify if a set of coordinates is a function
Range of a piecewise-defined function
Domain of a piecewise-defined function
Formal mapping notation
Find the range given a restricted domain
Find the implied domain of a function
Range of a single function
Domain of a single function
Sketching cubics
Sketching a circle
Sketching semi-circles
Sketching basic hyperbolas in the from y=a/x where a is a positive integer
Sketching exponentials
Sketching square root curves
Sketching the logarithmic graph
Sketch piecewise defined functions
Sketching graphs with a higher-order power of four or more
Sketch a function applying multiple transformations
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