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

which is a valid prediction about the continuous function f(x)?\no f(x) ≤ 0 over the interval (-∞, ∞).\no f(x) > 0 over the interval (-1, ∞).\no f(x) ≥ 0 over the interval -1, 1.\no f(x) < 0 over the interval (0, 2).\n\nx\tf(x)\n-3\t-15\n-2\t-5\n-1\t0\n0\t5\n1\t0\n2\t-5

which is a valid prediction about the continuous function f(x)?\no f(x) ≤ 0 over the interval (-∞, ∞).\no f(x) > 0 over the interval (-1, ∞).\no f(x) ≥ 0 over the interval -1, 1.\no f(x) < 0 over the interval (0, 2).\n\nx\tf(x)\n-3\t-15\n-2\t-5\n-1\t0\n0\t5\n1\t0\n2\t-5

Answer

Explanation:

Step1: Analyze option 1

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

Step2: Analyze option 2

Check $f(x)>0$ over $(-1,\infty)$. When $x = 2$, $f(2)= - 5<0$, so this option is false.

Step3: Analyze option 3

Check $f(x)\geq0$ over $[-1,1]$. When $x=-1,f(-1) = 0$; when $x = 0,f(0)=5$; when $x = 1,f(1)=0$. So $f(x)\geq0$ for $x\in[-1,1]$, this option is true.

Step4: Analyze option 4

Check $f(x)<0$ over $(0,2)$. When $x = 1$, $f(1)=0$, so this option is false.

Answer:

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