From the minimum value of the independent variable to its maximum.
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Generally speaking, yes. The variable x is generally used as the independent variable. And y is generally the variable the depends on the value of x. So in most examples the x axis and the "independent" axis are the same.
Inferential Statistics
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x is a letter often used as a variable. It can be in the range or the domain. However, in elementary algebra, the variable x is most often used for the domain and f(x) =y for the range.
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.