Reciprocal Graphs - Sketching (CIE A Level Maths: Pure 1)

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Reciprocal Graphs - Sketching

What are reciprocal graphs?

  • Reciprocal graphs involve equations with an x term on the denominator e.g. 1 over x
  • There are two basic reciprocal graphs to know for A level

 y space equals space 1 over x and  y equals 1 over x squared 

  • The second one of these is always positiveReciprocal Graphs - Sketching Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

More reciprocal graphs

  • You also need to recognise graphs where the numerator is not one

Reciprocal Graphs - Sketching Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

  • The sign of a shows which part of the graph the curves are located
  • The size of a shows how steep the curves are
    • The closer a is to 0 the more L-shaped the curves are

    Reciprocal Graphs - Sketching Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes 

    • horizontal, y = 0 (x-axis)
    • vertical, x = 0 (y-axis)All have two asymptotes

How do I sketch a reciprocal graph?

Reciprocal Graphs - Sketching Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

 

STEP 1        Use the sign of “a” to locate the curves

and use the size of “a” to gauge the steepness of the curve

STEP 2        Sketch the graph

STEP 3        Label the points x = 1 and x = -1 as a guide to the scale of your graph

STEP 4        Draw asymptotes with a dotted line Draw asymptotes with dotted lines


  • These graphs do not intercept either axis
  • Graph transformations of them could cross the axes (see Translations)

Worked example

Reciprocal Graphs - Sketching Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.