• Mathematics Advanced
  • Year 11

Functions and Relations

approx. 14 hrs

12 topics

46 concepts

Become proficient in Functions and Relations to enhance your performance in Mathematics in the HSC.

Available in
NSW

Overview

The content covered in Year 11 Functions and Relations is aligned with the NSW Mathematics syllabus.  In Functions and Relations, students learn the concept of a function and a relation, and the relationship between a function and its graph. We help students demonstrate 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 12 topics, broken down into 46 concepts.

  • Function and Relations 6 concepts

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

    2. Even and odd functions

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

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

    5. Finding the output of a piecewise defined function

    6. Identify if a set of coordinates is a function

  • Domain and Range 4 concepts

    1. Domain of absolute value functions

    2. Range of absolute value functions

    3. Range of a single function

    4. Domain of a single function

  • Sketching Cubic Functions 5 concepts

    1. Sketch a cubic function applying reflection of the graph across the x or y axis

    2. Sketch a cubic function with dilation

    3. Sketch a cubic function applying vertical translation of the graph

    4. Sketch a cubic function applying horizontal translation of the graph

    5. Sketching cubics

  • Sketching Power Functions 5 concepts

    1. Sketch a power function applying reflection of the graph across the x or y axis

    2. Sketch a power function applying horizontal translation of the graph

    3. Sketch a power function with dilation

    4. Sketch a power function applying vertical translation of the graph

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

  • Sketching Hyperbolic Functions 7 concepts

    1. Sketch a hyperbola applying vertical translation of the graph

    2. Sketch a hyperbola applying horizontal translation of the graph

    3. Sketch a hyperbola with dilation

    4. Sketch a hyperbola applying reflection of the graph across the x or y axis

    5. Determine the equations of asymptotes

    6. Finding points of intersection of a line with a hyperbola

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

  • Sketching Circles 5 concepts

    1. Find the radius and centre of a circle given the equation or graph

    2. Find the radius and centre of a circle by completing the square

    3. Finding points of intersection of a line with a circle

    4. Sketching a circle

    5. Sketching semi-circles

  • Sketching Exponential Functions 5 concepts

    1. Sketch an exponential function applying vertical translation of the graph

    2. Sketch an exponential function applying reflection of the graph across the x or y axis

    3. Sketch an exponential function applying horizontal translation of the graph

    4. Sketch an exponential function with dilation

    5. Sketching exponentials

  • Sketching logarithms 2 concepts

    1. Sketch a basic logarithmic function

    2. Sketch a logarithmic function with transformations

  • Composite Functions 1 concept

    1. Sketch piecewise defined functions

  • Sketch absolute value functions 2 concepts

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

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

  • 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

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

Reporting

  • 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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