Chapter 7: Functions
Function is a relation in which each element of the domain is paired with exactly one element of the range. It means that for every X value on the coordinate plane, there is one and only one Y value. If a second Y value exists for the same X value, the graph is not a function.
Before we dive into the discussions of the functions, we need to talk little more about the coordinate plane. Each coordinate on the coordinate plane is made up of X coordinate and Y coordinate. Two coordinates are equal if both its X and Y coordinates are the same. This is called the Equality of ordered pairs. It states that for all real numbers a, b, c, and d, (a, b) = (c, d) if and only if a = c and b = d. A relation is a set of ordered pairs.
A relation is function if and only if each element of the domain is paired with exactly one element of the range. The domain is represented in X coordinate and the range is represented in Y coordinate. A relation is a one to one function if and only if each element of the domain is associated with a unique element of the range, and each element of the range is associated with a unique element of the domain. This means that the inverse of a function is also a function. There are mainly three types of functions. They are linear functions, polynomial functions, and exponential and logarithm functions.
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