• 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

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime