GraphsDiagram

The Hyperbola y = 1/x

Part of Reciprocal Graphs — GCSE Mathematics

This diagram covers The Hyperbola y = 1/x within Reciprocal Graphs for GCSE Mathematics. 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 be a useful differentiator on mixed-topic papers. It is section 3 of 11 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 3 of 11

Practice

11 questions

Recall

10 flashcards

The Hyperbola y = 1/x

Keep building this topic

Read this section alongside the surrounding pages in Reciprocal Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Reciprocal Graph Essentials Understanding Asymptotes Closer and Closer, but Never Touching Finding k and the Equation

Practice Questions for Reciprocal Graphs

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

Quick Recall 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

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Reciprocal Graph Essentials

Understanding Asymptotes