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.
Topic position
Section 10 of 11
Practice
11 questions
Recall
10 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.