Question

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

x	f(x)
-6	8
-4	2
-2	0
0	-2
2	-1
4	0
6	4

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.

Step2: Analyze the given data

As \(x\) increases from \(-6\) to \(-2\), \(f(x)\) decreases (\(8\) to \(0\)). As \(x\) increases from \(-2\) to \(2\), \(f(x)\) continues to decrease (\(0\) to \(-1\)). As \(x\) increases from \(2\) to \(4\), \(f(x)\) increases (\(-1\) to \(0\)). So the function changes its direction of increase/decrease at \(x = 2\).

Answer:

C. \((2,-1)\)