Last updated on Oct 23, 2026

Reciprocal and Modulus Graphs (AQA A-Level Further Maths): Quizzes

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Reciprocal and Modulus Graphs

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What happens at $x = a$ on $y = \frac{1}{f(x)}$ if $f(a) = 0$ ?

The graph has a vertical asymptote

If $f(x)$ is negative, what is the sign of $\frac{1}{f(x)}$ ?

Negative

At which points do $y = f(x)$ and $y = \frac{1}{f(x)}$ intersect?

Where $f(x) = \pm 1$

If $f(x)$ is increasing, what happens to $\frac{1}{f(x)}$ ?

It decreases

A maximum of $f(x)$ becomes what in $\frac{1}{f(x)}$ ?

A minimum point

If $0 < f(x) < 1$ , what is true about $\frac{1}{f(x)}$ ?

$\frac{1}{f(x)} > 1$

What does $|x|$ represent?

Distance from the origin

To sketch $y = |f(x)|$ , what do you do to negative parts of $f(x)$ ?

Reflect them in the x-axis

A minimum at $(2, -5)$ on $f(x)$ becomes what on $|f(x)|$ ?

A maximum at $(2, 5)$

As $f(x) \to \infty$ , what happens to $\frac{1}{f(x)}$ ?

It approaches zero

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Complex Numbers 1

Complex Numbers 2

Algebra and Series

Curve Sketching 1

Curve Sketching 2

Integration 1

Integration 2

Matrices 1

Matrices 2

Vectors 1

Vectors 2

Series

Differential Equations

Numerical Methods

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Matrices 2

Vectors 1

Vectors 2

Series

Differential Equations

Numerical Methods

Explore AQA A-Level Further Maths Exam Questions by Topics

Complex Numbers 1

Complex Numbers 2

Algebra and Series

Curve Sketching 1

Curve Sketching 2

Integration 1

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Matrices 1

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Vectors 1

Vectors 2

Series

Differential Equations

Numerical Methods

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Matrices 2

Vectors 1

Vectors 2

Series

Differential Equations

Numerical Methods

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