Types of Graphs (Edexcel GCSE Maths)

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 ()

    • 

  • Exponential ()

    • 

• 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

How do I draw exponential growth and decay?

• The equation represents exponential growth when

  • represents exponential decay when

    • is positive but less than 1

• Both of these graphs:

  • have a horizontal asymptote at

  • do not have a vertical asymptote

  • have a -intercept of

• The graph of is a similar shape to , but there are some differences

  • It is first stretched vertically by

  • It is then shifted units upwards

    • Therefore it has a horizontal asymptote at

    • and a -intercept of

• For example, a population may be modelled as , where is the population and represents time

  • This is an exponential decay as

  • The initial population (when ) will be 400 + 100 = 500

    • The -intercept is (0, 500)

  • Over a long period of time (large -value) the population will settle to 100

    • The asymptote is at

• Exponential decay can also be identified by a negative power using index laws

  • so is the model above

  • This has the form where