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

which is a valid prediction about the continuous function f(x)? f(x)≥0 over the interval 5, ∞). f(x)≤0 over the interval -1, ∞). f(x)>0 over the interval (-∞, 1). f(x)<0 over the interval (-∞, -1). x f(x) -5 8 -3 4 -1 0 1 -2 3 -2 5 0 7 4

which is a valid prediction about the continuous function f(x)? f(x)≥0 over the interval 5, ∞). f(x)≤0 over the interval -1, ∞). f(x)>0 over the interval (-∞, 1). f(x)<0 over the interval (-∞, -1). x f(x) -5 8 -3 4 -1 0 1 -2 3 -2 5 0 7 4

Answer

Explanation:

Step1: Analyze option 1

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

Step2: Analyze option 2

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

Step3: Analyze option 3

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

Step4: Analyze option 4

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

Answer:

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