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Exponential and Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

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Exponential and Logarithmic Functions

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For $f(x) = 2^{x-5}$ , which direction has the graph shifted from $f(x) = 2^x$ ?

Right by 5 units

What is the horizontal asymptote of $g(x) = 3^x + 4$ ?

$y = 4$

Which equation represents $f(x) = 5^x$ reflected over the x-axis?

$g(x) = -5^x$

Which equation represents $f(x) = 2^x$ reflected over the y-axis?

$g(x) = 2^{-x}$

What is the domain of $g(x) = \log_2(x - 3)$ ?

$(3, \infty)$

What is the vertical asymptote of $g(x) = \log_5(x + 2)$ ?

$x = -2$

For $g(x) = 4 \times 3^x$ , what is the horizontal asymptote?

$y = 0$

Which equation represents $f(x) = \log_3 x$ dilated vertically by factor 2?

$g(x) = 2\log_3 x$

What is the equation for $f(x) = 2^x$ shifted right 1 and down 3?

$g(x) = 2^{x-1} - 3$

What is the range of $g(x) = 5^x - 2$ where base $5 > 1$ ?

$(-2, \infty)$

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Exponential and Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

For f(x)=2x−5f(x) = 2^{x-5}f(x)=2x−5, which direction has the graph shifted from f(x)=2xf(x) = 2^xf(x)=2x?

What is the horizontal asymptote of g(x)=3x+4g(x) = 3^x + 4g(x)=3x+4?

Which equation represents f(x)=5xf(x) = 5^xf(x)=5x reflected over the x-axis?

Which equation represents f(x)=2xf(x) = 2^xf(x)=2x reflected over the y-axis?

What is the domain of g(x)=log⁡2(x−3)g(x) = \log_2(x - 3)g(x)=log2​(x−3)?

What is the vertical asymptote of g(x)=log⁡5(x+2)g(x) = \log_5(x + 2)g(x)=log5​(x+2)?

For g(x)=4×3xg(x) = 4 \times 3^xg(x)=4×3x, what is the horizontal asymptote?

Which equation represents f(x)=log⁡3xf(x) = \log_3 xf(x)=log3​x dilated vertically by factor 2?

What is the equation for f(x)=2xf(x) = 2^xf(x)=2x shifted right 1 and down 3?

What is the range of g(x)=5x−2g(x) = 5^x - 2g(x)=5x−2 where base 5>15 > 15>1?

Explore HSC SSCE Mathematics Advanced Revision Notes 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 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 $f(x) = 2^{x-5}$ , which direction has the graph shifted from $f(x) = 2^x$ ?

What is the horizontal asymptote of $g(x) = 3^x + 4$ ?

Which equation represents $f(x) = 5^x$ reflected over the x-axis?

Which equation represents $f(x) = 2^x$ reflected over the y-axis?

What is the domain of $g(x) = \log_2(x - 3)$ ?

What is the vertical asymptote of $g(x) = \log_5(x + 2)$ ?

For $g(x) = 4 \times 3^x$ , what is the horizontal asymptote?

Which equation represents $f(x) = \log_3 x$ dilated vertically by factor 2?

What is the equation for $f(x) = 2^x$ shifted right 1 and down 3?

What is the range of $g(x) = 5^x - 2$ where base $5 > 1$ ?