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Assuming that y is a function of x, that follows from the definition of a function. For each x-value, there can only be one y-value. The definition of a function is that (in this case), for every value of "x", a value of "y" can be calculated unambiguously. In the more general case, for every combination of the independent variables, a single value for the dependent variable can be calculated unambiguously.

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Q: Why a function can have at most one y-intercept?
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