• Mathematical Methods
  • Year 11

Functions and Graphs

approx. 14 hrs

5 topics

34 concepts

Build mastery in Functions and Graphs to demonstrate proficiency in assessment and examination tasks.

Available in


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.

Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 34 concepts.

  • Set Notation 9 concepts

    1. Writing and interpreting elements of a set

    2. Writing and interpreting subsets

    3. Writing and interpreting set difference

    4. Writing and interpreting the empty set

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

    6. Writing and interpreting infinite sets

    7. Writing and interpreting interval notation

    8. Writing and interpreting sets of numbers

    9. Writing and interpreting intersection of more than one set

  • Function and Relations 6 concepts

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

    2. Even and odd functions

    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

  • Domain and Range of Functions 7 concepts

    1. Range of a piecewise-defined function

    2. Domain 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. Range of a single function

    7. Domain 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 non-linear function on the number plane

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

    7. Sketching basic hyperbolas in the from y=a/x where a is a positive integer

    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

  • Transformation of Graphs 1 concept

    1. Sketch a function applying multiple transformations

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 Graphs


  • 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

Ready to start this program?

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We'll book in your first session and match you to an expert tutor

Starting at

$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

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