GCSE Maths (Edexcel)

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Shape of a Reciprocal Graph

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Algebra Graphs

Shape of a Reciprocal Graph

4:48 More Graphs
Spec A12 A14
Previous Shape of a Cubic Graph Next Kinematic Graphs
  • A reciprocal function contains a term that is a reciprocal of x
  • A reciprocal graph has a positive and negative portion
  • As x increases, y decreases in a reciprocal graph
  • As x decreases and becomes close to zero, y increases in a reciprocal graph
  • Reciprocal graphs have two lines of symmetry
  • The lines of symmetry split the graph into two symmetrical halves
  • The first line of symmetry for the reciprocal function y is 1 over x is y = x
  • The second line of symmetry for the reciprocal function y is 1 over x is y = -x
  • Reciprocal functions can be positive or negative
  • The graph of a positive reciprocal has positive y values when x is positive and negative y values when x is negative
  • The graph of a negative reciprocal has negative y values when x is positive and positive y values when x is negative
  • Regardless of the sign of the reciprocal function, the graphs have the same lines of symmetry
  • Changing the size of the numerator in a reciprocal function changes the curvature of the graph
  • A larger numerator makes the graph less curved and further away from the origin
  • A smaller numerator makes the graph more curved and closer to the origin

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