A relation is a set of ordered pairs. eg. (1, 3), (1, 5), (2, 6), (-1, 6) and (-4, 1) is a relation. This can be plotted on a number plane:
A function is a special type of relation where for every x value there is only ONE y value. The above example is not a function, as an x value of 1 gives 2 different y values of 3 and 5. eg. (1, 3), (2, 6), (-1, 6) and (-4, -1) is a function.
If ordered pairs follow a pattern or rule, then the function can be written as an equation. eg. (-1, 0), (0, 1), (1, 2) satisfy the equation y = x + 1.
Vertical Line Test
If a set of ordered pairs is graphed on the number plane, there is a way of checking if they form a function. eg. In the above example, there are two y values for one x value. On a number plane, they lie in a vertical line:
In general, if any x value gives more than one y value, then these points lie in a vertical line. If there is only one y value for an x value, then no point will lie vertically above another.
Even functions are symmetrical about the y-axis.
Odd functions have point symmetry. Rotating 180 degrees about the origin gives the same graph.
The x-intercept is where a graph cuts the x-axis. The value of y is 0 everywhere along the x-axis.
The y-intercept is where a graph cuts the y-axis. The value of x is 0 everywhere along the y-axis.
The domain is the set of all possible x values, whereas the range is the set of all possible y values.
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