A Guassian function has a top in the middle and it's ends reach until infinity but the graph never touches the x axis. The location of the top depends on the parameters used.
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It has no special name - other than a normal (or Gaussian) distribution graph.
shape
It's like a bell curve; there's a high point in the middle with both sides dropping off symmetrically away from it and then flattening out as you move away from the drop offs.
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.
It looks like a parabola which looks like a U shape.