HSC Advanced Functions_Graphs

Anchor_Mathematics, Jun 15, 2025

This book contains several pages and applets covering the graphs in the NSW HSC, along with methods of transformations,

Table of Contents

  1. Transformations of a Line and a Parabola
    1. Graph the Line
    2. Line in gradient intercept form
    3. Parabola in factored form
    4. Parabola from completed square
  2. Transformations of a Cubic
    1. Cubic in factored form
    2. Cubic in translation form
  3. Transformations of other Functions
    1. Square root
    2. Hyperbola - Inverse Variation
    3. Absolute Value
    4. Polynomial degree 4 - quartic in factor form
    5. Polynomial degree 5 - quintic in factor form
    6. Exponential graph with variable Base
    7. Exponential graph base e
    8. Log graph with variable base
    9. Log Natural graph base e
  4. Transformations of Circles and Semi-Circles
    1. Circle centre (h,k), radius r
    2. Semi-Circle based at the origin
  5. Reflections across the axes
    1. Reflections of an unknown function

1.

Transformations of a Line and a Parabola

  • 1. Graph the Line
  • 2. Line in gradient intercept form
  • 3. Parabola in factored form
  • 4. Parabola from completed square

1.1.

Graph the Line

Drag points A and B so the line matches the equation.
– Steve Phelps

1.2.

–

1.3.

–

1.4.

–

2.

Transformations of a Cubic

  • 1. Cubic in factored form
  • 2. Cubic in translation form

2.1.

Cubic in factored form

Cubic in the form y = a(x - b)(x - c)(x - d)
– Anchor_Mathematics

2.2.

–

3.

Transformations of other Functions

  • 1. Square root
  • 2. Hyperbola - Inverse Variation
  • 3. Absolute Value
  • 4. Polynomial degree 4 - quartic in factor form
  • 5. Polynomial degree 5 - quintic in factor form
  • 6. Exponential graph with variable Base
  • 7. Exponential graph base e
  • 8. Log graph with variable base
  • 9. Log Natural graph base e

3.1.

Square root

Graph in the form y = a(x - h)^0.5
– Anchor_Mathematics

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

4.

Transformations of Circles and Semi-Circles

  • 1. Circle centre (h,k), radius r
  • 2. Semi-Circle based at the origin

4.1.

Circle centre (h,k), radius r

– Anchor_Mathematics

4.2.

–

5.

Reflections across the axes

  • 1. Reflections of an unknown function

5.1.

Reflections of an unknown function

Reflection across x and y axes
– Anchor_Mathematics

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