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\tf(x)\n-3\t-15\n-2\t-5\n-1\t0\n0\t5\n1\t0\n2\t-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\tf(x)\n-3\t-15\n-2\t-5\n-1\t0\n0\t5\n1\t0\n2\t-5

Answer

Explanation:

Step1: Analyze option 1

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

Step2: Analyze option 2

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

Step3: Analyze option 3

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

Step4: Analyze option 4

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

Answer:

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