which statement is true about the given function?\n○ ( f(x)>0 ) over the interval ((-infty,3)).\n○ ( f(x)>0…

Explanation:

Step1: Analyze the graph

Observe the y - values of the function for different x - values.

Step2: Check the interval $(-\infty,3)$

For $x\in(-\infty,3)$, some parts of the graph are below the x - axis (where $y = f(x)<0$) and some parts are above the x - axis (where $y = f(x)>0$).

Step3: Check the interval $(-\infty,\infty)$

The graph has parts above and below the x - axis. It is not always positive or always negative over $(-\infty,\infty)$.

Step4: Determine the correct statement

By looking at the graph, we can see that $f(x)<0$ over some sub - intervals of $(-\infty,3)$. But overall, $f(x)$ is not always positive or negative over $(-\infty,3)$ or $(-\infty,\infty)$. However, we can see that $f(x)<0$ for some values in $(-\infty,3)$.

Answer:

$f(x)<0$ over the interval $(-\infty,3)$ is the correct statement among the given options.