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Multiple Transformations (HSC SSCE Mathematics Advanced): Quizzes

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Multiple Transformations

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If no order is given, which transformations apply first?

Dilations and reflections

For $g(x) = -\frac{2}{x+3} + 1$ , where is the vertical asymptote?

$x = -3$

If $f(x) = \frac{1}{x}$ is translated up 1 unit, what is the horizontal asymptote?

$y = 1$

What is the domain of $g(x) = -\frac{2}{x+3} + 1$ ?

$x \neq -3$

For $g(x) = -4(x-2)^2 - 1$ , what is the vertex?

$(2, -1)$

What is the range of $g(x) = -4(x-2)^2 - 1$ ?

$y \leq -1$

To reflect a function over the y-axis, what do you replace $x$ with?

$-x$

For horizontal dilation by factor $\frac{1}{2}$ , replace $x$ with:

$2x$

To translate a function left by 3 units, replace $x$ with:

$x + 3$

Why does $g(x) = -4(x-2)^2 - 1$ have no x-intercepts?

Vertex at $(2, -1)$ below x-axis

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Multiple Transformations (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

If no order is given, which transformations apply first?

For g(x)=−2x+3+1g(x) = -\frac{2}{x+3} + 1g(x)=−x+32​+1, where is the vertical asymptote?

If f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ is translated up 1 unit, what is the horizontal asymptote?

What is the domain of g(x)=−2x+3+1g(x) = -\frac{2}{x+3} + 1g(x)=−x+32​+1?

For g(x)=−4(x−2)2−1g(x) = -4(x-2)^2 - 1g(x)=−4(x−2)2−1, what is the vertex?

What is the range of g(x)=−4(x−2)2−1g(x) = -4(x-2)^2 - 1g(x)=−4(x−2)2−1?

To reflect a function over the y-axis, what do you replace xxx with?

For horizontal dilation by factor 12\frac{1}{2}21​, replace xxx with:

To translate a function left by 3 units, replace xxx with:

Why does g(x)=−4(x−2)2−1g(x) = -4(x-2)^2 - 1g(x)=−4(x−2)2−1 have no x-intercepts?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

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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 $g(x) = -\frac{2}{x+3} + 1$ , where is the vertical asymptote?

If $f(x) = \frac{1}{x}$ is translated up 1 unit, what is the horizontal asymptote?

What is the domain of $g(x) = -\frac{2}{x+3} + 1$ ?

For $g(x) = -4(x-2)^2 - 1$ , what is the vertex?

What is the range of $g(x) = -4(x-2)^2 - 1$ ?

To reflect a function over the y-axis, what do you replace $x$ with?

For horizontal dilation by factor $\frac{1}{2}$ , replace $x$ with:

To translate a function left by 3 units, replace $x$ with:

Why does $g(x) = -4(x-2)^2 - 1$ have no x-intercepts?