Zman Kietilipooskie

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Domain of a specific Piece-wise graph

So basically the question goes down to the question that if mx+b>A and Qx+C≤A and > means that the value can get inifinitely close to the A value, doesnt that mean that the two lines are not connected? Doesnt that mean that the domain is (-∞,A]υ(A,∞) and not (-∞,∞)?

In other words there is a distance between the slope mx+b>A and the slope Qx+C≤A and it is not zero, right?

Here let me try and re word (I don't think I did a good job the first time) it if the first slope is less than or equal to A and then the second slope is more then A, then isn't there a gap (that is infinitely small) between the A and the second slope because the second slope never actually touches A?

For the domain to be (-infinity, infinity) the slopes must both be less than and equal to or more then or equal to, otherwise the domain has an inifinitely small and infinitely decreasing in distance as it approaches A but never actually touches it.