A graph is simply a drawing of the coordinate
plane with points
plotted on it. These points all have
coordinates
(*x*, *y*)
. In the graph of a
function, the y-coordinate has
the value
*f* (*x*)
, meaning the coordinates of the graph of a function are
(*x*, *f* (*x*))
. The possible values of
*x*
are elements of the
domain of the function, and the
possible values for
*f* (*x*)
, or
*y*
, are the elements of the
range of the function. Viewing
the graph, a given x-coordinate can be selected, and the value of
*y*
at that
point is the value of the function at that
*x*
-coordinate. Below are the graphs
for some simple functions.

Figure %: Some simple functions are graphed

Because a function can produce only one output for a given input, it is easy to
determine whether a given graph is a graph of a function or not. If a vertical
line can be placed somewhere in the coordinate plane such that it intersects
with the graph twice, the graph is not a function. Two intersections with a
vertical line signify that for a given value of
*x*
, there are two possible values
of
*f* (*x*)
, which by definition is impossible for a function. This method for
testing a potential function is called the vertical line test.

The graphs of the trigonometric
functions are plots of points whose
coordinates are
(*x*, *f* (*x*))
, with
*x*
being an angle measure in
radians. The y-coordinate,
*f* (*x*)
, is a real
number--specifically, it is the ratio
that defines the value of a given trigonometric function. In the next
section we'll see what the graphs of the six
trigonometric functions look like.

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