This deep dive covers Understanding Asymptotes 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 4 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 11
Practice
11 questions
Recall
10 flashcards
Understanding Asymptotes
An asymptote is a line that the curve approaches but never reaches or crosses.
For y = k/x, there are two asymptotes:
- Vertical asymptote: x = 0 — when x = 0, we get k ÷ 0, which is undefined. The curve gets infinitely close to the y-axis but never touches it.
- Horizontal asymptote: y = 0 — as x becomes very large (positive or negative), y = k/x approaches zero but never reaches it. The curve gets infinitely close to the x-axis but never crosses it.
Important: a curve can NEVER cross its asymptote. If you draw the curve touching or crossing the axes, you will lose marks.
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.
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
11 questions on Reciprocal Graphs — practise free
Instant marking, adaptive difficulty, and 10 spaced repetition flashcards. Free until your GCSEs.
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