0580/22 Feb/Mar 2021, Question 21: Reciprocal Functions
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
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The question, in short
On blank axes, sketch the graphs of two functions, y = 1/x and y = 4ˣ, showing their key features.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Sketch y = 1/x on the axes, showing its shape and behaviour near the axes.
- 1y = 1/x is a reciprocal graph with two branches
- 2One branch in the first quadrant (x > 0, y > 0), one in the third quadrant (x < 0, y < 0)
- 3Each branch gets close to both axes but never touches them
AnswerCorrect sketch
Part (b) · 2 marks
Sketch y = 4ˣ on the axes, showing its shape and where it crosses the y-axis.
- 1y = 4ˣ is an exponential curve
- 2It passes through (0, 1) and rises steeply for x > 0
- 3For x < 0 it gets close to the x-axis but stays above it
AnswerCorrect sketch
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