Last updated on Oct 23, 2026

Exponential Graphs (HSC SSCE Mathematics Advanced): Quizzes

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Exponential Graphs

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Why must the base $a \neq 1$ in exponential function $y = k(a^x)$ ?

It creates horizontal line $y = k$

What is the $y$ -intercept of $y = k(a^x)$ ?

$(0, k)$

What is the horizontal asymptote for basic exponential functions?

$y = 0$

What is the domain of exponential functions?

All real numbers

When does exponential growth occur in $y = k(a^x)$ ?

When $a > 1$

When does exponential decay occur in $y = k(a^x)$ ?

When $0 < a < 1$

For $y = k(a^x)$ with $a > 1$ , what happens as $x \to \infty$ ?

$y \to \infty$

What is the range of $y = k(a^x)$ when $k > 0$ ?

$y > 0$

What is $y = 2^{-x}$ equivalent to?

$y = (\frac{1}{2})^x$

How are $y = 2^x$ and $y = (\frac{1}{2})^x$ related?

Reflections across the $y$ -axis

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Exponential Graphs (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

Why must the base a≠1a \neq 1a=1 in exponential function y=k(ax)y = k(a^x)y=k(ax)?

What is the yyy-intercept of y=k(ax)y = k(a^x)y=k(ax)?

What is the horizontal asymptote for basic exponential functions?

What is the domain of exponential functions?

When does exponential growth occur in y=k(ax)y = k(a^x)y=k(ax)?

When does exponential decay occur in y=k(ax)y = k(a^x)y=k(ax)?

For y=k(ax)y = k(a^x)y=k(ax) with a>1a > 1a>1, what happens as x→∞x \to \inftyx→∞?

What is the range of y=k(ax)y = k(a^x)y=k(ax) when k>0k > 0k>0?

What is y=2−xy = 2^{-x}y=2−x equivalent to?

How are y=2xy = 2^xy=2x and y=(12)xy = (\frac{1}{2})^xy=(21​)x related?

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

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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

Why must the base $a \neq 1$ in exponential function $y = k(a^x)$ ?

What is the $y$ -intercept of $y = k(a^x)$ ?

When does exponential growth occur in $y = k(a^x)$ ?

When does exponential decay occur in $y = k(a^x)$ ?

For $y = k(a^x)$ with $a > 1$ , what happens as $x \to \infty$ ?

What is the range of $y = k(a^x)$ when $k > 0$ ?

What is $y = 2^{-x}$ equivalent to?

How are $y = 2^x$ and $y = (\frac{1}{2})^x$ related?