Reciprocal Graphs (Cambridge (CIE) IGCSE International Maths): Revision Note

Reciprocal Graphs

What is a reciprocal graph?

• A reciprocal graph is of the form

  • It does not have a y-intercept

  • and does not have any roots

  • This means that the curve does not cross either the x- or y-axes

What are the asymptotes on a reciprocal graph?

• An asymptote is a line on a graph that a curve becomes closer and closer to but never touches

  • These may be horizontal or vertical lines

• A reciprocal graph has two asymptotes

  • A horizontal asymptote along the x-axis (with equation )

    • This is the limiting value of y when the value of x gets very large (either positive or negative)

  • A vertical asymptote along the y-axis (with equation )

    • This shows the problem of trying to divide by zero

What about graphs of the form y = a/x + b ?

• The reciprocal graph, (where and are both constants)

  • is the same shape as

  • but is shifted upwards by units

    • would be shifted up by 2 units

    • would be shifted down by 3 units

  • This means the horizontal asymptote also shifts up by units,

    • The equation of the horizontal asymptote is

    • would have a horizontal asymptote of

    • would have a horizontal asymptote of

  • The vertical asymptote remains along the y-axis

    • The equation of the vertical asymptote is

    • would have a vertical asymptote of