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No. A function is a "graph" the survives the "vertical line test". Namely, it is for every x in its domain, there can be one and only one f(x) in its co-domain. An ellipse clearly fails it at everywhere except it's two vertex.

But an ellipse can be thought as two separate functions. A standard ellipse relation, x^2 / a + (y)^2 / b = 1, can be thought as two separate real functions of y1 and y2. where y1 = -y2 exactly.

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Q: Is an ellipse a function
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