This common misconceptions covers Common Misconceptions 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 10 of 11 in this topic. Use this common misconceptions to connect the idea to the wider topic before moving on to questions and flashcards.
⚠️ Common Misconceptions
Misconception 1: "The two branches of y = 1/x meet at the origin"
The two branches of a reciprocal graph NEVER meet — the origin is the one point they approach most closely but can never reach, because y = 1/0 is undefined. The graph has a gap at x = 0. The two branches exist in separate quadrants, each approaching but never touching either axis. Drawing a curve that passes through or near the origin on a reciprocal graph is a serious error.
Misconception 2: "The curve crosses the x-axis somewhere far to the right"
The curve y = k/x NEVER crosses the x-axis — the x-axis (y = 0) is a horizontal asymptote. As x gets larger and larger, y = k/x gets closer and closer to zero but never actually equals zero. Similarly, the curve never crosses the y-axis (vertical asymptote at x = 0). If you draw the curve touching or crossing either axis, you have made an error.
Misconception 3: "y = 3/x and y = −3/x have the same graph"
These are reflections of each other in the x-axis, not the same graph. y = 3/x (k > 0) has branches in quadrants 1 and 3. y = −3/x (k < 0) has branches in quadrants 2 and 4. The sign of k determines which quadrants the branches appear in. Both have the same absolute value of k (and therefore the same "size" of branches), but they are mirror images.
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.