which is a valid prediction about the continuous function f(x)? f(x) ≥ 0 over the interval 5, ∞). f(x) ≤ 0…

which is a valid prediction about the continuous function f(x)? f(x) ≥ 0 over the interval 5, ∞). f(x) ≤ 0 over the interval -1, ∞). f(x) > 0 over the interval (-∞, 1). f(x) < 0 over the interval (-∞, -1).

which is a valid prediction about the continuous function f(x)? f(x) ≥ 0 over the interval 5, ∞). f(x) ≤ 0 over the interval -1, ∞). f(x) > 0 over the interval (-∞, 1). f(x) < 0 over the interval (-∞, -1).

Answer

Explanation:

Step1: Analyze option 1

We have data - points. For (x = 5), (f(5)=0) and for (x = 7), (f(7)=4>0). Since the function is continuous, for (x\geq5), (f(x)\geq0).

Step2: Analyze option 2

At (x = 7), (f(7)=4>0) and (7\in[- 1,\infty)), so (f(x)\leq0) over ([-1,\infty)) is false.

Step3: Analyze option 3

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

Step4: Analyze option 4

At (x=-5), (f(-5)=8>0) and (-5\in(-\infty,-1)), so (f(x)<0) over ((-\infty,-1)) is false.

Answer:

(f(x)\geq0) over the interval ([5,\infty))