• Mathematics Advanced
  • Year 11

Functions and Relations

approx. 14 hrs

13 topics

59 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 13 topics, broken down into 59 concepts.

  • 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

  • Sketching logarithms 2 concepts

    1. Sketch a basic logarithmic function

    2. Sketch a logarithmic function with transformations

  • 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

  • Sketching Cubic Functions 5 concepts

    1. Sketch a cubic function with dilation

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

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

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

    5. Sketching cubics

  • Sketching Power Functions 5 concepts

    1. Sketch a power function with dilation

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

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

    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 with dilation

    2. Sketch a hyperbola applying horizontal translation of the graph

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

    4. Sketch a hyperbola applying vertical translation of the graph

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

    6. Determine the equations of asymptotes

    7. Sketching hyperbolas

  • Sketching Exponential Functions 5 concepts

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

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

    3. Sketch an exponential function with dilation

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

    5. Sketching exponentials

  • Sketching Circles 5 concepts

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

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

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

    4. Sketching semi-circles

    5. Sketching a circle

  • Composite Functions 2 concepts

    1. Sketch piecewise defined functions

    2. 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

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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