Types of Graphs (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Types of graphs

What types of graphs do I need to know?

• You need to be able to recognise, sketch, and interpret the following types of graph:

  • Linear ()

    • or

  • Quadratic ()

    • 

  • Cubic ()

    • or

  • Reciprocal ()

    • 

• You must also be able to recognise the three basic trigonometric graphs, covered in the Trigonometry section

Where are the asymptotes on reciprocal graphs?

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

  • These may be horizontal or vertical

• The reciprocal graph, (where is a constant)

  • does not have a y-intercept

  • and does not have any roots

• This graph has two asymptotes

  • A horizontal asymptote at the x-axis: 

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

  • A vertical asymptote at the y-axis: 

    • This is the value that causes the denominator to be zero

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

  • is the same shape as

  • but is shifted upwards by units

    • would be shifted down by 3 units

  • This means the horizontal asymptote also shifts up by units

    • The vertical asymptote remains on the y-axis