Learning Lab

Download the functions and graphs worksheets to improve your skills in these areas.

• 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.