Question

Over what interval is f(x) negative? Justify your answer.

Answer 1

Answer in interval notation is  (-3, 1)

This is the same as saying -3 < x < 1

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Explanation:

Since y = f(x), this means we're looking for points on the red curve such that they have a negative y coordinate. Visually, we're looking for points that are below the horizontal x axis.

These points are shown in the diagram below. I've marked the section we're after in blue. This blue section spans from x = -3 to x = 1. We exclude both endpoints because each x value leads to f(x) = 0, but we want f(x) values smaller than zero.