the independent variable
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x is independent because of the x axis and y axis on a coordinate plane.
Only if y = 0 then it is the entire x-axis. Otherwise, for y = k and k is any number except zero, the graph is parallel to the x-axis and does not intersect.
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.
x axis
On the Cartesian plane x is the horizontal axis and y is the vertical axis and they intersect at right angles at the origin (0,0))