In simple terms, if a vertical line meets a graph in more than one place it is not a function.
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A graph is a function if any vertical line intersects it at most once.
If a vertical line intersects the graph at more than one point then it is not a function.
They mean the graph/function is decreasing.
The Mandelbrot graph is generated iteratively and so is a function of a function of a function ... and in that sense it is a composite function.
The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.