which is a valid prediction about the continuous function f(x)?\no f(x) ≤ 0 over the interval (-∞, ∞).\no…

Explanation:

Step1: Analyze option 1

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

Step2: Analyze option 2

$f(2)= - 5<0$, 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 valid.

Step4: Analyze option 4

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

Answer:

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