Jnit 1 Test
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Merenanovg
01:25:54
\begin{tabular}{|c|c|}
\hline$x$ & $f(x)$ \\
\hline-3 & -15 \\
\hline-2 & -5 \\
\hline-1 & 0 \\
\hline 0 & 5 \\
\hline 1 & 0 \\
\hline 2 & -5 \\
\hline
\end{tabular}
Which is a valid prediction about the continuous function $f(x)$ ?
$f(x) \leq 0$ over the interval $(-\infty, \infty)$.
$f(x)> 0$ over the interval $(-1, \infty)$.
$f(x) \geq 0$ over the interval $[-1,1]$
$f(x)< 0$ over the interval $(0,2)$.

Step 1 ：The question is asking us to predict the behavior of the function \(f(x)\) over certain intervals. We are given a table of values for \(f(x)\) at certain points. We need to check each of the given options against the values in the table to see which one is valid.

Step 2 ：Let's define the function values as \(f(x)\) = {-3: -15, -2: -5, -1: 0, 0: 5, 1: 0, 2: -5}.

Step 3 ：Let's define the options as {'\(f(x) \leq 0\) over the interval \((-\infty, \infty)\)': False, '\(f(x) > 0\) over the interval \((-1, \infty)\)': False, '\(f(x) \geq 0\) over the interval \([-1,1]\)': True, '\(f(x) < 0\) over the interval \((0,2)\)': False}.

Step 4 ：From the above, we can see that the only valid option is '\(f(x) \geq 0\) over the interval \([-1,1]\)'.

Step 5 ：Final Answer: The valid prediction about the continuous function \(f(x)\) is \(f(x) \geq 0\) over the interval \([-1,1]\). So, the final answer is \(\boxed{f(x) \geq 0 \text{ over the interval } [-1,1]}\).