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

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

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

Answer

Explanation:

Step1: Analyze the first option

For the interval $[5,\infty)$, when $x = 5$, $f(5)=0$ and when $x = 7$, $f(7)=4$. Since the function is continuous, $f(x)\geq0$ for $x\in[5,\infty)$.

Step2: Analyze the second option

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

Step3: Analyze the third option

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

Step4: Analyze the fourth option

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

Answer:

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