What are reciprocal graphs?

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

• The second one of these is always positive

More reciprocal graphs

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

• 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

  

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

How do I sketch a reciprocal graph?

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)