Use a calculator to graph the functions y = –3|x – 2| and y = x3 – 3x – 3. How many points of intersection do the functions share?

Split the absolute-value graph at x = 2. For x < 2, y = −3|x − 2| becomes y = 3x − 6; equating this to x³ − 3x − 3 gives x³ − 6x + 3 = 0, which has two roots less than 2. For x ≥ 2, the graph is y = −3x + 6; equating the functions gives x³ = 9, with one solution x = ∛9 that is at least 2. Thus there are three intersection points, so the answer is 3.

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