x f(x) -6 8 -4 2 -2 0 0 -2 2 -1 4 0 6 4 which is a possible turning point for the continuous function f(x)…

x f(x) -6 8 -4 2 -2 0 0 -2 2 -1 4 0 6 4 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 which is a possible turning point for the continuous function f(x)? (-2, 0) (0, -2) (2, -1) (4, 0)

Answer

Explanation:

Step1: Understand 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

The function values change as follows: $f(-6)=8$, $f(-4) = 2$, $f(-2)=0$, $f(0)=-2$, $f(2)=-1$, $f(4)=0$, $f(6)=4$. The function is decreasing from $x=-6$ to $x = 0$ and then starts increasing from $x = 0$ to $x=6$.

Step3: Identify the turning - point

The point where the function changes from decreasing to increasing is around $x = 0$. Among the given options, the point $(0,-2)$ is the one that lies in the domain of the function's change in behavior.

Answer:

$(0,-2)$