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 | f(x)\n-3 | -15\n-2 | -5\n-1 | 0\n0 | 5\n1 | 0\n2 | -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 | f(x)\n-3 | -15\n-2 | -5\n-1 | 0\n0 | 5\n1 | 0\n2 | -5

Answer

Answer:

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

Explanation:

Step1: Analyze option A

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

Step2: Analyze option B

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

Step3: Analyze option C

For $x=-1$, $f(-1)=0$; for $x = 0$, $f(0)=5$; for $x = 1$, $f(1)=0$. So $f(x)\geq0$ over $[-1,1]$.

Step4: Analyze option D

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