Last updated on Oct 23, 2026

Reciprocal and Absolute Value Functions (HSC SSCE Mathematics Advanced): Flashcards

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Reciprocal and Absolute Value Functions

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General form of transformed reciprocal function

$g(x) = \frac{l}{x - a} + b$

Vertical asymptote of $g(x) = \frac{l}{x - a} + b$

$x = a$

Horizontal asymptote of $g(x) = \frac{l}{x - a} + b$

$y = b$

Domain of $g(x) = \frac{l}{x - a} + b$

$x \neq a$

Range of $g(x) = \frac{l}{x - a} + b$

$y \neq b$

General form of transformed absolute value function

$g(x) = l|x - a| + b$

Vertex of $g(x) = l|x - a| + b$

$(a, b)$

Domain of $g(x) = l|x - a| + b$

All real numbers

Range of $g(x) = l|x - a| + b$ when $l > 0$

$[b, \infty)$

Effect of $l < 0$ on absolute value graph

V-shape flips upside down (reflects over x-axis)

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Reciprocal and Absolute Value Functions (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

General form of transformed reciprocal function

Vertical asymptote of g(x)=lx−a+bg(x) = \frac{l}{x - a} + bg(x)=x−al​+b

Horizontal asymptote of g(x)=lx−a+bg(x) = \frac{l}{x - a} + bg(x)=x−al​+b

Domain of g(x)=lx−a+bg(x) = \frac{l}{x - a} + bg(x)=x−al​+b

Range of g(x)=lx−a+bg(x) = \frac{l}{x - a} + bg(x)=x−al​+b

General form of transformed absolute value function

Vertex of g(x)=l∣x−a∣+bg(x) = l|x - a| + bg(x)=l∣x−a∣+b

Domain of g(x)=l∣x−a∣+bg(x) = l|x - a| + bg(x)=l∣x−a∣+b

Range of g(x)=l∣x−a∣+bg(x) = l|x - a| + bg(x)=l∣x−a∣+b when l>0l > 0l>0

Effect of l<0l < 0l<0 on absolute value graph

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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

Vertical asymptote of $g(x) = \frac{l}{x - a} + b$

Horizontal asymptote of $g(x) = \frac{l}{x - a} + b$

Domain of $g(x) = \frac{l}{x - a} + b$

Range of $g(x) = \frac{l}{x - a} + b$

Vertex of $g(x) = l|x - a| + b$

Domain of $g(x) = l|x - a| + b$

Range of $g(x) = l|x - a| + b$ when $l > 0$

Effect of $l < 0$ on absolute value graph