Sketching cubic & reciprocal graphs
AQA GCSE Maths revision on Sketching cubic & reciprocal graphs. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
When sketching the graph of y = 1/x, why does the graph never touch the y-axis?
- A) Division by zero is undefined
- B) The graph is a straight line
- C) The value of y must be positive
- D) The graph has a maximum point
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Answer: Division by zero is undefined
In the function y = 1/x, substituting x = 0 results in division by zero, which is undefined in mathematics. This creates a vertical asymptote where the curve approaches the axis but never reaches or crosses it.
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Question 2
A student sketches y = x^3 and draws a graph that passes through (1, 1), (2, 4), and (-1, -1). Identify the error.
- A) The point (2, 4) is incorrect
- B) The graph should be a straight line
- C) The graph cannot be in the third quadrant
- D) The point (-1, -1) is incorrect
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Answer: The point (2, 4) is incorrect
The student has confused y = x^3 with y = x^2. Since 2 cubed is 8, the point (2, 8) should be on the graph, not (2, 4).
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Question 3
What is the correct term for the invisible lines that a reciprocal graph approaches but never touches?
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Answer: Asymptote
An asymptote is a line such that the distance between the curve and the line approaches zero as one or both of the coordinates tend to infinity. Reciprocal functions like y = 1/x have both a horizontal and a vertical asymptote.
Want to test yourself on the remaining cards for this topic?
13 more questions on Sketching cubic & reciprocal graphs — plus mistakes tracking and spaced repetition across the whole Maths spec.