- Choose x-values on BOTH sides of zero (e.g. −4, −2, −1, 1, 2, 4)
- NEVER include x = 0 — it is undefined
- Calculate y = k/x for each x-value
- Plot points in both the positive and negative regions
- Draw TWO separate smooth curves, each approaching but never touching the axes
Example table for y = 6/x:
| x | −6 | −3 | −2 | −1 | 1 | 2 | 3 | 6 |
|---|---|---|---|---|---|---|---|---|
| y | −1 | −2 | −3 | −6 | 6 | 3 | 2 | 1 |
Note how the branches are symmetric — the curve in Q1 mirrors the curve in Q3.
This deep dive covers Drawing a Reciprocal Graph from a Table of Values 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 6 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Reciprocal Graphs
The graph of y = 1/x has an asymptote along the x-axis. What does this mean?
Explain why the graph y = 5/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
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.