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If the function is to be continuous, then it is a function if

x3 + 2 ≤ 0 or if x3 + 2 ≥ 0 but not both.

That is, when x3 ≤ -2 or x3 ≥ -2.

So x ≤ -1.2599 or x ≥ -1.2599 (approx).

The graph is like a parabola that has been tipped on its side and the above procedure takes either the top half of the parabola or the bottom half. That way you can be sure that no vertical line intersects the graph in more than one place. However, that can also be achieved by taking a segment of the curve above the x-axis, then the next segment from below, then above and below and so on.

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11y ago

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