You use the vertical line test. If you can draw a vertical line though the graph and it intersects it only once, it is a function. If the line crosses the graphs more than once it is not.
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A graph is represents a function if for every value x, there is at most one value of y = f(x).
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.
For a 2-dimensional graph if there is any value of x for which there are more than one values of the graph, then it is not a function. Equivalently, any vertical line can intersect the a function at most once.
The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.
A linear function would be represented by a straight line graph, so if it's not a straight line, it's nonlinear