Last updated on Oct 23, 2026

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

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Reciprocal and Absolute Value Functions

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For $g(x) = \frac{3}{x - 5} + 2$ , what is the vertical asymptote?

$x = 5$

For $g(x) = \frac{-2}{x + 1} - 4$ , what is the horizontal asymptote?

$y = -4$

What is the domain of $g(x) = \frac{1}{x - 3} + 7$ ?

$x \neq 3$

What is the range of $g(x) = \frac{2}{x + 1} - 5$ ?

$y \neq -5$

What transformation does $l < 0$ cause in $g(x) = \frac{l}{x - a} + b$ ?

Reflects over the $x$ -axis

For $g(x) = 3|x + 2| - 1$ , what is the vertex?

$(-2, -1)$

What is the domain of $g(x) = -2|x - 4| + 3$ ?

All real numbers

If $l = 2$ in $g(x) = 2|x - 1| + 5$ , what is the range?

$[5, \infty)$

What does $|l| > 1$ do to the shape of $g(x) = l|x - a| + b$ ?

Makes V-shape narrower

In $g(x) = \frac{1}{x - a} + b$ , if $a = -3$ , how does the graph shift?

Shifts left by 3 units

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

Practise the questions

For g(x)=3x−5+2g(x) = \frac{3}{x - 5} + 2g(x)=x−53​+2, what is the vertical asymptote?

For g(x)=−2x+1−4g(x) = \frac{-2}{x + 1} - 4g(x)=x+1−2​−4, what is the horizontal asymptote?

What is the domain of g(x)=1x−3+7g(x) = \frac{1}{x - 3} + 7g(x)=x−31​+7?

What is the range of g(x)=2x+1−5g(x) = \frac{2}{x + 1} - 5g(x)=x+12​−5?

What transformation does l<0l < 0l<0 cause in g(x)=lx−a+bg(x) = \frac{l}{x - a} + bg(x)=x−al​+b?

For g(x)=3∣x+2∣−1g(x) = 3|x + 2| - 1g(x)=3∣x+2∣−1, what is the vertex?

What is the domain of g(x)=−2∣x−4∣+3g(x) = -2|x - 4| + 3g(x)=−2∣x−4∣+3?

If l=2l = 2l=2 in g(x)=2∣x−1∣+5g(x) = 2|x - 1| + 5g(x)=2∣x−1∣+5, what is the range?

What does ∣l∣>1|l| > 1∣l∣>1 do to the shape of g(x)=l∣x−a∣+bg(x) = l|x - a| + bg(x)=l∣x−a∣+b?

In g(x)=1x−a+bg(x) = \frac{1}{x - a} + bg(x)=x−a1​+b, if a=−3a = -3a=−3, how does the graph shift?

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Explore HSC SSCE Mathematics Advanced Flashcards by Topics

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Solve Equations

Introduction to Functions and Relations

Linear Functions

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Probability

Data

Introduction to Rates of Change

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Logarithmic Functions

For $g(x) = \frac{3}{x - 5} + 2$ , what is the vertical asymptote?

For $g(x) = \frac{-2}{x + 1} - 4$ , what is the horizontal asymptote?

What is the domain of $g(x) = \frac{1}{x - 3} + 7$ ?

What is the range of $g(x) = \frac{2}{x + 1} - 5$ ?

What transformation does $l < 0$ cause in $g(x) = \frac{l}{x - a} + b$ ?

For $g(x) = 3|x + 2| - 1$ , what is the vertex?

What is the domain of $g(x) = -2|x - 4| + 3$ ?

If $l = 2$ in $g(x) = 2|x - 1| + 5$ , what is the range?

What does $|l| > 1$ do to the shape of $g(x) = l|x - a| + b$ ?

In $g(x) = \frac{1}{x - a} + b$ , if $a = -3$ , how does the graph shift?