Defining a Function
Rectangular coordinate systems. A rectangular coordinate system consists of x-axis (the horizontal line) and y-axis (the vertical line) intersecting at the origin. An ordered pair
gives the x-coordinate 
and
the y-coordinate 
of a point
which lies away from the origin along the concerned axes.
Functions.
A function 
is a “correspondence” from each element 
of a set 
to “exactly” one element 
of a set 
.
The domain of is the set itself,
but the range of must be defined as a subset 
of consisting
of all possible values 
for in .
In mathematical terms the range of can be expressed as
For example, both the domain and the range of a linear function
are given by the set of entire real numbers.
In other words,
.
Alternative definition of function.
A function with domain can be viewed as the set
on the rectangular coordinate system.
Vertical line test.
Every “vertical line” should intersect the graph of
in at most one point.
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