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Reciprocal Graphs

Revise Reciprocal Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears less often, but it can still pick up marks when it appears in mixed-topic papers.

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Closer and Closer, but Never Touching

Introduction 2

Reciprocal Graph Essentials

Key Facts 3

The Hyperbola y = 1/x

Diagram 4

Understanding Asymptotes

Deep Dive 5

Finding k and the Equation

Deep Dive 6

Drawing a Reciprocal Graph from a Table of Values

Deep Dive 7

Reciprocal Graphs and Inverse Proportion

Key Facts 8

Exam Tips for Reciprocal Graphs

Exam Tips 9

Worked Examples

Notes 10

Common Misconceptions

Misconceptions 11

Topic Summary: Reciprocal Graphs

Summary

Sample Flashcards

What does the graph of y = 1/x look like?

A hyperbola — two separate curved branches. - One branch in the top-right (positive x, positive y) - One branch in the bottom-left (negative x, negative y) The curve gets closer and closer to both axes but never touches them.

What is an asymptote and where are they on y = k/x?

An asymptote is a line the curve approaches but never reaches or crosses. For y = k/x: - Vertical asymptote: x = 0 (the y-axis) - The function is UNDEFINED when x = 0 - Horizontal asymptote: y = 0 (the x-axis) - y never equals zero for any finite x

Sample Questions

The graph of y = 1/x has an asymptote along the x-axis. What does this mean?

A. The graph touches the x-axis at x = 0
B. The graph crosses the x-axis at x = 1
C. The graph gets closer and closer to the x-axis but never reaches it
D. The graph is a straight line along the x-axis

1 markfoundation

Explain why the graph y = 5/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

2 markshigher

exam-style questions

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