It could be the x-axis.
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X intercepts
It depends on what x is. If (x, y) were the scores on the roll of two dice, with x the first die and y the second, the set of all possible values of x would be {1, 2, 3, 4, 5, 6} - a finite set of integers. In other cases, x could be any real number.
You do not graph range and domain: you can determine the range and domain of a graph. The domain is the set of all the x-values and the range is is the set of all the y-values that are used in the graph.
No. The set of x-values are the domain for only g. This will result in a set of images, which will be g(x). This set of g(x) values are the domain of f.
Usually the set of x values.