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

which is a valid prediction about the continuous function f(x)? f(x) ≤ 0 over the interval (-∞, ∞). f(x) > 0 over the interval (-1, ∞). f(x) ≥ 0 over the interval -1, 1. f(x) < 0 over the interval (0, 2).

which is a valid prediction about the continuous function f(x)? f(x) ≤ 0 over the interval (-∞, ∞). f(x) > 0 over the interval (-1, ∞). f(x) ≥ 0 over the interval -1, 1. f(x) < 0 over the interval (0, 2).

Answer

Explanation:

Step1: Analyze each option

Check the values of (f(x)) in the given table for each interval.

Step2: Analyze option 1

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

Step3: Analyze option 2

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

Step4: 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.

Step5: Analyze option 4

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

Answer:

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