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Reciprocal Graph Essentials

Part of Reciprocal Graphs — GCSE Mathematics

This key facts covers Reciprocal Graph Essentials 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 2 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 11

Practice

11 questions

Recall

10 flashcards

Reciprocal Graph Essentials

  • General form: y = k/x (also written y = kx⁻¹)
  • Shape: hyperbola — two separate curved branches
  • k > 0: branches in quadrants 1 (top-right) and 3 (bottom-left)
  • k < 0: branches in quadrants 2 (top-left) and 4 (bottom-right)
  • Asymptotes: x = 0 (y-axis) and y = 0 (x-axis)
  • Undefined at x = 0: division by zero is impossible
  • Key property: x × y = k (the product of coordinates is constant)

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.

Closer and Closer, but Never TouchingThe Hyperbola y = 1/xUnderstanding AsymptotesFinding 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 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
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.

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Closer and Closer, but Never Touching

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The Hyperbola y = 1/x