Last updated on Sep 21, 2026

Absolute Value Functions (HSC SSCE Mathematics Advanced): Flashcards

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Absolute Value Functions

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General form of absolute value function

$f(x) = |ax + b|$ , $a \neq 0$

Graph shape of absolute value function

V-shaped

Vertex coordinates of $f(x) = |ax + b|$

$\left(-\frac{b}{a}, 0\right)$

Domain of $f(x) = |ax + b|$

All real numbers ( $\mathbb{R}$ )

Range of $f(x) = |ax + b|$

$y \geq 0$

How to find vertex x-coordinate

Solve $ax + b = 0$

Line of symmetry for $f(x) = |ax + b|$

$x = -\frac{b}{a}$

Solutions count for $|ax + b| = k$ if $k > 0$

Two solutions

Solutions count for $|ax + b| = k$ if $k = 0$

One solution

Solutions count for $|ax + b| = k$ if $k < 0$

No solutions

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Absolute Value Functions (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

General form of absolute value function

Graph shape of absolute value function

Vertex coordinates of f(x)=∣ax+b∣f(x) = |ax + b|f(x)=∣ax+b∣

Domain of f(x)=∣ax+b∣f(x) = |ax + b|f(x)=∣ax+b∣

Range of f(x)=∣ax+b∣f(x) = |ax + b|f(x)=∣ax+b∣

How to find vertex x-coordinate

Line of symmetry for f(x)=∣ax+b∣f(x) = |ax + b|f(x)=∣ax+b∣

Solutions count for ∣ax+b∣=k|ax + b| = k∣ax+b∣=k if k>0k > 0k>0

Solutions count for ∣ax+b∣=k|ax + b| = k∣ax+b∣=k if k=0k = 0k=0

Solutions count for ∣ax+b∣=k|ax + b| = k∣ax+b∣=k if k<0k < 0k<0

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

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Trigonometric Identities and Equations

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Introduction to Rates of Change

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Exponential Functions

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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 Quizzes 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

Vertex coordinates of $f(x) = |ax + b|$

Domain of $f(x) = |ax + b|$

Range of $f(x) = |ax + b|$

Line of symmetry for $f(x) = |ax + b|$

Solutions count for $|ax + b| = k$ if $k > 0$

Solutions count for $|ax + b| = k$ if $k = 0$

Solutions count for $|ax + b| = k$ if $k < 0$