Sketching cubic & reciprocal graphs
Edexcel GCSE Maths revision on Sketching cubic & reciprocal graphs. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
What is the shape of the graph y = 1/x?
- A) A hyperbola with two distinct branches
- B) A parabola with a single turning point
- C) A straight line passing through origin
- D) A cubic curve with two turning points
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Answer: A hyperbola with two distinct branches
The graph of y = 1/x is a standard reciprocal graph known as a hyperbola, which features two branches located in the first and third quadrants. A common misconception is to confuse this with a parabola, which is the characteristic shape of a quadratic function.
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Question 2
How many times does the graph y = x^3 - 4x cross the x-axis?
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Answer: 3
By factorising the equation to x(x - 2)(x + 2) = 0, we identify the roots at x = 0, x = 2, and x = -2. Therefore, the graph intersects the x-axis at exactly three distinct points.
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Question 3
Which coordinate represents the vertical asymptote of the graph y = 1/(x - 3)?
- A) The line where x is equal to positive three
- B) The line where x is equal to negative three
- C) The line where y is equal to positive three
- D) The line where y is equal to negative three
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Answer: The line where x is equal to positive three
The vertical asymptote occurs where the function is undefined, which happens when the denominator (x - 3) equals zero. Solving this gives x = 3, which is a vertical line that the graph approaches but never touches.
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.