Overview
Defining Functions:
Function is a relation Such that for each value of x there is only One and One value Y. (Relation is a set of ordered pairs)
The Value of x on graph is called the domain of the function and the Value of y on the graph is called range of the function.
Example:
{ (1,2),(3,4),(5,6),(6,1),(2,2)}Each ordered pair have a different first element therefore it is a function
Example:
F(x)=6x+7
This is a proper function since , because for each value substituted for x there is one and only one value for f(x) Domain=[all real numbers] Reange=[all real numbers]
Example
{(1,2),(3,2),(1,4)}
- This is a relation but not a function.
- Since there is a repeated value for X (Domain).
- For each X value there should only be one value of Y
- In other words for a single Domain there cannot be 2 Ranges if its a function
When we are talking about function , we must remember that there is a Unique range value for a single domain Value.
Figure 1 Figure 2
To test for a Function we perform a vertical line test on its graph.If the vertical line intersects the graph on 2 points as shown in figure 2 than it shall not be a real function.
However there can be 2 same range values for different domain values as shown in figure 2.
This Figure is another Example of a graph which is not a function since it fails the Vertical line test (there are two points of intersection for the vertical line drawn thus the test proves that the given graph of (x,y) relation is not a function.)
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