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A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output is called as a function.

Vertical line test:

If all vertical lines intersect a curve at most once then the curve represents a function.

Yes,

A single point on the graph is a function.

We know that every input in the domain has exactly one output.

Suppose $(m,n)$ is the point on the graph.

Graphically if vertical line cross the graph at most once then the graph is the graph of a function.

If we consider the point $(m,n)$and we can draw the vertical line y = n then the point $(m,n)$ is represent a function otherwise it is undefined.

For example: Let (2, 3) is a point on the graph.

and f(x) = 3 is a function if x = 2 otherwise it is undefined.

Yes, a graph that consists of a single point is the graph of a function.

For example:f(x) = 3 is a function if x = 2 otherwise it is undefined.