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Reciprocal Graphs and Inverse Proportion

Part of Reciprocal Graphs — GCSE Mathematics

This key facts covers Reciprocal Graphs and Inverse Proportion 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 7 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 7 of 11

Practice

11 questions

Recall

10 flashcards

Reciprocal Graphs and Inverse Proportion

  • y = k/x means y is inversely proportional to x: y ∝ 1/x
  • As x doubles, y halves; as x triples, y becomes one-third
  • The product x × y is the same at every point: xy = k
  • Lines of symmetry of y = k/x (k > 0): y = x and y = −x (diagonal lines through origin)
  • y = k/x and y = −k/x are reflections of each other in the x-axis

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.

Drawing a Reciprocal Graph from a Table of ValuesExam Tips for Reciprocal GraphsCloser and Closer, but Never TouchingReciprocal Graph Essentials

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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Drawing a Reciprocal Graph from a Table of Values

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Exam Tips for Reciprocal Graphs