Yes and it will be a straight line intercepting y at -1 and parallel to the x axis
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I don't understand your question but y=3x is the function of a graph, to graph the function you would plug points into the function such as x=0, x=1, x=-1 and you would find the y values at each point so that you can graph it. In this case the graph is a parabola which has a u shape.
No, it would not.
Since the function depends on 4 variables (assuming that p and P are the same variable), the full graph would require 5 dimensions. You can, however, graph something like a cross-section for the graph, in the sense that you keep most of the variables constant, and study the dependency of the function on a single variable at a time.
Yes, that is a shifted tanX graph, just as you would shift any graft.
It would have a downhill slope from left to right