This key facts covers Reciprocal Graph Essentials 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 2 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Reciprocal Graph Essentials
- General form: y = k/x (also written y = kx⁻¹)
- Shape: hyperbola — two separate curved branches
- k > 0: branches in quadrants 1 (top-right) and 3 (bottom-left)
- k < 0: branches in quadrants 2 (top-left) and 4 (bottom-right)
- Asymptotes: x = 0 (y-axis) and y = 0 (x-axis)
- Undefined at x = 0: division by zero is impossible
- Key property: x × y = k (the product of coordinates is constant)
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.