Which would most likely be graphed using a continuous graph?

A continuous graph is a graph where it does not break apart and all points are connected, for example, y=x. You get a line intersecting the origin that increases to infinity, and all points are connected.

What isn't a continuous (discontinuous graph) graph is a graph  is a graph with asymptotes. Asymptotes usually occur when the variable is in the denominator, for example y = 1/x. Dividing anything by 0 would make an error, a no solution, so if x was 0 then there would be no solution, no point on the graph. So the graph would be discontinuous at x=0.