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As long as the line represented on the graph has no vertical segments then it may be represented by a function.

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That is not enough.

y = sqrt(x) has no vertical segments but it is not a function in the mathematical sense.

A function cannot map an x value to more than one y value. Clearly, the above function maps x to -sqrt(x) and +sqrt(x) and so is not a function. However, there no vertical segment. No matter how close you get to x = 0, there is still a curve and the segment is not vertical.

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13y ago

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Q: How do you know if a graph is a function or not?
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