Last updated on Oct 23, 2026

Horizontal and Vertical Translations (HSC SSCE Mathematics Advanced): Quizzes

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Horizontal and Vertical Translations

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What stays unchanged when a graph undergoes a translation?

Shape and size

For $y = f(x - 5)$ , in which direction does the graph move?

5 units right

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

3 units left

For $y = f(x) + 7$ , in which direction does the graph move?

7 units up

Which coordinates change in a horizontal translation?

x-coordinates

Which coordinates change in a vertical translation?

y-coordinates

For $y = (x - 2)^2 + 3$ , where does the vertex of $y = x^2$ move to?

$(2, 3)$

What is $f(x) = x^2 + 1$ after a horizontal translation 3 units left?

$(x + 3)^2 + 1$

What is $f(x) = 2x$ after a vertical translation 4 units down?

$2x - 4$

What happens to the slope when $y = 2x$ is translated vertically?

Slope stays 2, lines are parallel

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Horizontal and Vertical Translations (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What stays unchanged when a graph undergoes a translation?

For y=f(x−5)y = f(x - 5)y=f(x−5), in which direction does the graph move?

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

For y=f(x)+7y = f(x) + 7y=f(x)+7, in which direction does the graph move?

Which coordinates change in a horizontal translation?

Which coordinates change in a vertical translation?

For y=(x−2)2+3y = (x - 2)^2 + 3y=(x−2)2+3, where does the vertex of y=x2y = x^2y=x2 move to?

What is f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 after a horizontal translation 3 units left?

What is f(x)=2xf(x) = 2xf(x)=2x after a vertical translation 4 units down?

What happens to the slope when y=2xy = 2xy=2x is translated vertically?

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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 $y = f(x - 5)$ , in which direction does the graph move?

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

For $y = f(x) + 7$ , in which direction does the graph move?

For $y = (x - 2)^2 + 3$ , where does the vertex of $y = x^2$ move to?

What is $f(x) = x^2 + 1$ after a horizontal translation 3 units left?

What is $f(x) = 2x$ after a vertical translation 4 units down?

What happens to the slope when $y = 2x$ is translated vertically?