which is a possible turning point for the continuous function f(x)?\n(-2,0)\n(0,-2)\n(2,-1)\n(4,0)\nx\tf(x)\n…

Explanation:

Step1: Recall turning - point concept

A turning point of a continuous function is a point where the function changes from increasing to decreasing or vice - versa. This usually occurs where the derivative is zero or undefined. For a discrete set of points like in the table, we look for a change in the trend of the function values.

Step2: Analyze the trend of f(x)

As (x) goes from (-6) to (-2), (f(x)) decreases ((8) to (0)). As (x) goes from (-2) to (2), (f(x)) continues to decrease ((0) to (-1)). As (x) goes from (2) to (4), (f(x)) increases from (-1) to (0).

Step3: Identify the turning - point

The function changes its trend from decreasing to increasing between (x = 2) and (x = 4). Among the given points, the point ((4,0)) is where the function has completed the transition from decreasing to increasing.

Answer:

((4,0))