Functions and Graphs for Intermediate Maths
Master graphing with clear visuals, guided examples, and practice. Aligned to VCE, HSC, QLD, WA & SACE. Great for revision or acceleration!
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? Course Description
Functions and Graphs for Intermediate Maths is a targeted course designed to help students excel in one of the most essential topics across senior high school mathematics curricula in Australia. Whether you’re studying VCE Maths Methods, NSW HSC Mathematics Advanced or Extension, QLD Mathematical Methods, WA ATAR Methods, or SACE Stage 2 Mathematical Methods, this course breaks down complex graphing skills into clear, structured lessons.
You’ll explore function notation, domain and range, graph transformations, and composite functions—all through visual and practical approaches. By the end, you’ll not only gain graphing fluency but also be well-prepared for higher-level topics like calculus, modelling, and probability.
Ideal for students aiming to consolidate their understanding of functions before moving on to more advanced concepts.
⭐ Key Features
- Curriculum-Aligned Across States Mapped to senior high school curricula including VCE Unit 3, HSC Advanced/Extension, QLD/WA/SA Methods.
- Step-by-Step Graphing Strategies Master sketching of linear, quadratic, cubic, exponential, logarithmic, and trigonometric functions with clarity and confidence.
- Visual + Algebraic Transformations Grasp shifts, stretches, reflections, and composite transformations with guided visual supports.
- Immediate Practice & Feedback Build intuition with practice questions after each concept, complete with worked solutions.
- Flexible for All Goals Perfect for revision, bridging gaps, or accelerating learning ahead of upcoming assessments or topics.
- Interactive Q&A + Optional 1-on-1 Tutoring Each course includes a built-in Q&A section. Ask questions where you’re stuck—our tutors will respond within the course. Need deeper support? 1-on-1 tutoring is available.
Additional fees apply for private sessions.
? Keyphrases
- Functions and Graphs
- Intermediate Maths Functions Course
- VCE Maths Methods Unit 3 & 4 Graphs
- NSW HSC Maths Advanced/Extension Graphs
- QLD Mathematical Methods Functions and Modelling
- WA ATAR Maths Methods Graphing and Applications
- SACE Stage 2 Mathematical Methods – Functions
- Senior High School Functions and Graphs
- Graphing Techniques and Transformations
1. Graphs and Properties of Functions
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1.1.1 Introduction to Graph Sketching -
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1.1.2 Sketching the Graph
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1.1.3 Properties of a Graph
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1.1.4 Introduction to Power Functions
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1.1.5 Drawing Power Functions (for Positive Integers) and its Graph Properties
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1.1.6 Drawing Power Functions (for Negative Integers) and its Graph Properties
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1.1.7 Drawing Power Functions (for n=1/k where k is a Positive Integer) and its Graph Properties
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1.1.8 Drawing Power Functions (for n=-1/k where k is a Positive Integer) and its Graph Properties
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1.1.9 Power Functions (for n=p/q where p, q are Positive Integers)
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1.1.10 Summary of Power Function Graph Properties
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1.1.11 Inverses of Power Functions
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1.1.12 Exponential Functions
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1.1.13 Logarithmic Functions
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1.1.14 Trigonometric Functions - Degrees and Radians
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1.1.15 Trigonometric Functions - Sine, Cosine and Tangent
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1.1.16 Trigonometric Functions - Symmetry Properties
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1.1.17 Trigonometric Functions - Other Properties
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1.1.18 Graphs of Sine and Cosine Functions
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1.1.19 Graphs of Tangent Functions
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1.1.20 Additional Graph Types - Circles
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1.1.21 Additional Graph Types - Ellipses (Not Required)
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1.1.22 Additional Graph Types - Inverted Parabolic Shapes
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Quiz - A1.1 Graphs and Properties of Functions
Starting Course
2. Polynomial Functions
3. Transformation of Graphs
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1.3.1 Transformation 1: Translation
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1.3.2 Transformation 2: Dilation
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1.3.3 Transformation 3: Reflection
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1.3.4 Illustrate Combination of Transformations
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1.3.5 Determine Combination of Transformations
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1.3.6 Transformations of Power Functions
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1.3.7 Transformations of Polynomial Functions
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1.3.8 Transformations of Exponential Functions
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1.3.9 Transformations of Logarithmic Functions
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1.3.10 Transformations of Sine and Cosine
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1.3.11 Transformations of Tangent
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1.3.12 Inverse Transformations
4. Relationship of Transformations
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1.4.1 Transformations with a Single Parameter
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1.4.2 Introduction to Matrices
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1.4.3 Matrix Addition, Subtraction, and Scalar Multiplication
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1.4.4 Matrix Multiplications
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1.4.5 The Identity Matrix
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1.4.6 Using Matrices for Transformations
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1.4.7 Composition of Mappings
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1.4.8 Inverse of 2x2 Matrices for Transformations
5. Real Life Applications Using Function Models
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1.5.1 Applications of Polynomial Functions
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1.5.2 Applications of Circular Functions
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1.5.3 Special Exponential Functions
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1.5.4 Special Logarithm Functions
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1.5.5 Composite Functions
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1.5.6 Sum and Product of Functions
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1.5.7 Graph Sketching for Sum of Functions
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1.5.8 Graph Sketching for Product of Functions
FAQ 1
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FAQ 2
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Course details
Duration
10 hours
Lectures
60
Video
9 hours
Quizzes
2
Level
Advanced
Basic info
- Course Title: Functions and Graphs for Intermediate Maths
- Level: Senior High School
- Suitable Curricula:
- VCE Maths Methods Unit 3 & 4
- NSW HSC Mathematics Advanced / Extension
- QLD Mathematical Methods
- WA ATAR Mathematics Methods
- SACE Stage 2 Mathematical Methods
- Mode: Online, Self-Paced
Intended audience
This course is designed for:
- Students across Australia studying:
- VCE, HSC, QLD, WA, or SACE senior maths pathways Students who want to:
- Strengthen graphing and function concepts before advancing to calculus or modelling
- Revise key topics ahead of assessments or final exams
- Bridge gaps in understanding due to curriculum transitions or missed lessons
- Get ahead with a clear, visual, and structured approach to graphing
- VCE, HSC, QLD, WA, or SACE senior maths pathways Students who want to:
- Ideal for both classroom support and independent learning
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