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0580/23 May/Jun 2021, Question 24: Reciprocal Functions

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks

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The question, in short

On the given axes, sketch the graphs of two functions, y = 2/x and y = 2⁻ˣ.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Sketch the graph of y = 2/x on the axes.

  1. 1Reciprocal graph with k = 2 > 0
  2. 2Draw a branch in the first quadrant and a branch in the third quadrant
  3. 3Both branches approach the axes but never touch them

AnswerCorrect sketch: reciprocal curve with one branch in the first quadrant and one in the third quadrant, approaching both axes

Part (b) · 2 marks

Sketch the graph of y = 2⁻ˣ on the axes.

  1. 1When x = 0, y = 1, so the curve crosses the y-axis at (0, 1)
  2. 2y increases steeply for negative x and decreases towards 0 for positive x
  3. 3The curve stays above the x-axis in the first and second quadrants

AnswerCorrect sketch: decreasing exponential curve crossing the y-axis at 1, approaching the x-axis as x increases

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Also searched as: 0580/23/M/J/21 · 0580_s21_qp_23 · 0580 s21 23 · question 24.
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