which is a valid prediction about the continuous function f(x)?\n○ f(x) ≤ 0 over the interval (-∞, ∞)\n○…

which is a valid prediction about the continuous function f(x)?\n○ f(x) ≤ 0 over the interval (-∞, ∞)\n○ f(x) > 0 over the interval (-1, ∞)\n○ f(x) ≥ 0 over the interval -1, 1\n○ f(x) < 0 over the interval (0, 2)\n\nx | f(x)\n-3 | -15\n-2 | -5\n-1 | 0\n0 | 5\n1 | 0\n2 | -5

which is a valid prediction about the continuous function f(x)?\n○ f(x) ≤ 0 over the interval (-∞, ∞)\n○ f(x) > 0 over the interval (-1, ∞)\n○ f(x) ≥ 0 over the interval -1, 1\n○ f(x) < 0 over the interval (0, 2)\n\nx | f(x)\n-3 | -15\n-2 | -5\n-1 | 0\n0 | 5\n1 | 0\n2 | -5

Answer

Answer:

C. (f(x)\geq0) over the interval ([- 1,1])

Explanation:

Step1: Analyze option A

When (x = 0), (f(0)=5>0), so (f(x)\leq0) over ((-\infty,\infty)) is false.

Step2: Analyze option B

When (x = 2), (f(2)= - 5<0), so (f(x)>0) over ((-1,\infty)) is false.

Step3: Analyze option C

For (x=-1), (f(-1) = 0); for (x = 0), (f(0)=5>0); for (x = 1), (f(1)=0). So (f(x)\geq0) over ([-1,1]) is true.

Step4: Analyze option D

When (x = 0), (f(0)=5>0), so (f(x)<0) over ((0,2)) is false.