Last updated on Sep 20, 2026

Advanced Applications of Transformations (HSC SSCE Mathematics Advanced): Quizzes

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Order of Transformations

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Which transformation shifts a graph without changing its shape or orientation?

Translation

For $y = f(x - 3)$ , in which direction does the graph move?

Right by 3 units

For $y = af(\frac{x}{k} - b) + c$ , which transformation is applied first?

Horizontal dilation

Transformations inside the function brackets affect which variable?

$x$ values

What does $y = f(-x)$ represent?

Reflection in the $y$ -axis

What happens when vertical dilation and vertical translation are applied in different orders?

Same result either order

For $f(x) = x^2$ , if horizontal dilation by 2 then translation right by 1, where is the vertex?

$(1, 0)$

For $f(x) = x^2$ , if translation right by 1 then horizontal dilation by 2, where is the vertex?

$(2, 0)$

What is the equation for reflection of $f(x)$ in the $x$ -axis?

$y = -f(x)$

For $f(x) = \frac{1}{x}$ , reflecting then translating up 2 gives which horizontal asymptote?

$y = 2$

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Advanced Applications of Transformations (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

Which transformation shifts a graph without changing its shape or orientation?

For y=f(x−3)y = f(x - 3)y=f(x−3), in which direction does the graph move?

For y=af(xk−b)+cy = af(\frac{x}{k} - b) + cy=af(kx​−b)+c, which transformation is applied first?

Transformations inside the function brackets affect which variable?

What does y=f(−x)y = f(-x)y=f(−x) represent?

What happens when vertical dilation and vertical translation are applied in different orders?

For f(x)=x2f(x) = x^2f(x)=x2, if horizontal dilation by 2 then translation right by 1, where is the vertex?

For f(x)=x2f(x) = x^2f(x)=x2, if translation right by 1 then horizontal dilation by 2, where is the vertex?

What is the equation for reflection of f(x)f(x)f(x) in the xxx-axis?

For f(x)=1xf(x) = \frac{1}{x}f(x)=x1​, reflecting then translating up 2 gives which horizontal asymptote?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

For $y = f(x - 3)$ , in which direction does the graph move?

For $y = af(\frac{x}{k} - b) + c$ , which transformation is applied first?

What does $y = f(-x)$ represent?

For $f(x) = x^2$ , if horizontal dilation by 2 then translation right by 1, where is the vertex?

For $f(x) = x^2$ , if translation right by 1 then horizontal dilation by 2, where is the vertex?

What is the equation for reflection of $f(x)$ in the $x$ -axis?

For $f(x) = \frac{1}{x}$ , reflecting then translating up 2 gives which horizontal asymptote?