• Mathematical Methods
  • Year 11

Functions and Relations

approx. 14 hrs

7 topics

42 concepts

Gain confidence and develop proficiency in Functions and Relations for success in Year 12 Mathematics.

Available in


The content covered in Year 11 Functions and Relations is aligned with the Australian curriculum.  In this program, we help students learn the concept of a function and a relation, and the relationship between a function and its graph. Students develop competence in sketching a graph by identifying its type, using the known properties and observing where the function increases or decreases, its symmetrical properties, domain, range and any points of discontinuity.

Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 42 concepts.

  • Domain and Range of Functions 7 concepts

    1. Domain of a piecewise-defined function

    2. Range of a piecewise-defined function

    3. Formal mapping notation

    4. Find the range given a restricted domain

    5. Find the implied domain of a function

    6. Domain of a single function

    7. Range of a single function

  • Set Notation 9 concepts

    1. Writing and interpreting elements of a set

    2. Writing and interpreting subsets

    3. Writing and interpreting intersection of more than one set

    4. Writing and interpreting the union of more than one set

    5. Writing and interpreting the empty set

    6. Writing and interpreting set difference

    7. Writing and interpreting sets of numbers

    8. Writing and interpreting infinite sets

    9. Writing and interpreting interval notation

  • Transformation of Graphs 1 concept

    1. Sketch a function applying multiple transformations

  • Regions in the Number Plane 3 concepts

    1. Sketch a region defined by a non-linear inequality

    2. Intersection of regions

    3. Sketch a region defined by a linear inequality

  • Domain and Range 5 concepts

    1. Find the implied domain of a function

    2. Domain of absolute value functions

    3. Range of absolute value functions

    4. Domain of a single function

    5. Range of a single function

  • Sketching Functions 11 concepts

    1. Sketching exponentials

    2. Sketching cubics

    3. Sketching semi-circles

    4. Sketching a circle

    5. Sketching the absolute value of a linear function on the number plane

    6. Sketching the absolute value of a non-linear function on the number plane

    7. Sketching hyperbolas

    8. Sketching the logarithmic graph

    9. Sketching square root curves

    10. Sketch piecewise defined functions

    11. Sketching graphs with a higher-order power of four or more

  • Function and Relations 6 concepts

    1. Even and odd functions

    2. Determine if a function is one-to-one

    3. Identify if a set of coordinates is a function

    4. Use function notation to find the output of a single function

    5. Use the vertical line test on a graph to decide whether it represents a function

    6. Finding the output of a piecewise defined function

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Functions and Relations


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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