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Functions and graphs

Functions and graphs provide a way to represent, analyse, and understand relationships between different quantities. If you are looking to improve your knowledge of this area, the linked resources are a great way to start.

  • Plotting points on a graph
    Graphs usually have points or markers on them. The location of this point is given by an ordered pair.
  • FG1 Functions and relations
    A relation is a set of ordered pairs.
  • FG2 Interval notation
    Often the domain of a function will be restricted to a subset of R. This subset is called an interval, and the end points are a and b.
  • FG3 Inverse notation
    If f-1(x) is the inverse function of a one-to-one function f(x) then f-1(x) is the set of ordered pairs obtained by interchanging the first and second elements in each ordered pair.
  • FG4 Absolute value functions
    The absolute value of a number x gives a measure of its size or magnitude regardless of whether it is positive or negative. If a number is plotted on a number line then its absolute value can be considered to be the distance from zero.
  • FG5 Hybrid functions
    Functions which have different rules for each subset of the domain are called hybrid functions. Sometimes they are referred to as piecewise defined functions.
  • FG6 Circular functions
    The trigonometric ratios that have been defined in right-angled triangles can be extended to angles greater than 90 degrees.
  • FG7 Linear graphs
    Understanding a linear graph is the simplest way of representing data or a functional relationship. This module explains the equations and visuals of a linear graph.
  • FG8 Quadratic graphs
    The graph of a quadratic function is called a parabola.
  • FG9 Graphs and transformations
    The known graphs of some simple functions and relations can be used to sketch related, but more complicated functions.
  • FG10 Graphs of sine and cosine functions
    Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1]. The graphs of both functions have an amplitude of 1 and a period of 2π radians.