## Functions and graphs

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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.

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