Question

which is a possible turning point for the continuous function f(x)?
(-3, -4)
(-2, -1)
(0, -5)
(1, -8)

x f(x)
-4 -6
-3 -4
-2 -1
-1 -2
0 -5
1 -8
2 -16

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 function's trend

From the table, when \(x=-4\), \(f(x)= - 6\); when \(x=-3\), \(f(x)=-4\); when \(x = - 2\), \(f(x)=-1\); when \(x=-1\), \(f(x)=-2\); when \(x = 0\), \(f(x)=-5\); when \(x = 1\), \(f(x)=-8\); when \(x = 2\), \(f(x)=-16\). The function is increasing from \(x=-4\) to \(x=-2\) (\(f(-4)=-6\), \(f(-3)=-4\), \(f(-2)=-1\)) and then decreasing from \(x=-2\) onwards (\(f(-1)=-2\), \(f(0)=-5\), \(f(1)=-8\), \(f(2)=-16\)).

Answer:

\((-2,-1)\)