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Exam Tips for Reciprocal Graphs

Part of Reciprocal Graphs — GCSE Mathematics

This exam tips covers Exam Tips for Reciprocal Graphs 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 8 of 11 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.

Topic position

Section 8 of 11

Practice

11 questions

Recall

10 flashcards

💡 Exam Tips for Reciprocal Graphs

  • Two separate branches: always draw two distinct curves — never a single connected curve that passes through or near the origin
  • Never touch the axes: the curves must approach but never reach the x-axis and y-axis
  • Identify quadrants from k: k > 0 → branches in Q1 and Q3; k < 0 → branches in Q2 and Q4
  • Find k using xy = k: any point on the curve gives the value of k
  • Never include x = 0 in a table of values — state it is undefined

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 Graphs and Inverse ProportionWorked ExamplesCloser 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 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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Reciprocal Graphs and Inverse Proportion

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Worked Examples