What is the graph of a function when it has no gaps or holes?

It is a continuous line whose shape depends upon what expression it is meant to represent.

The equation y = x would be a straight line passing through (0,0) and all the other points where the x and y co-ordinates were equal, including negative ones such as (-11,-11).

But if the equation has x squared in it the shape would be a parabola, while the graph of an equation with y cubed in it would have something like an S shape in it. More complex equations could produce many differently shaped lines.