x f(x) -3 -15 -2 -5 -1 0 0 5 1 0 2 -5 which is a valid prediction about the continuous function f(x)? f(x) ≤…

x f(x) -3 -15 -2 -5 -1 0 0 5 1 0 2 -5 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).

x f(x) -3 -15 -2 -5 -1 0 0 5 1 0 2 -5 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 option A

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

Step2: Analyze option B

$f(1) = 0$, 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

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

Answer:

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