For the function f(x) shown below, which of the following represents the interval over which f(x)< 0?

For a given function f(x) we want to see in which interval we have f(x) < 0.

We will see that the correct option is the first one:

-2 < x < 4

Let's see how to get the solution.

To see in which interval the function is negative, we need to see over which interval the graph of the function is below the horizontal axis.

By looking at the graph, we can see that this happens in the interval (-2, 4)

Where we used an open interval because we want f(x) strictly smaller than 0, not equal.

Then the interval is:

-2 < x < 4

Thus the correct option is the first one.

if you want to learn more, you can read:

link

(1)

Step-by-step explanation:

Note that f(x) < 0 below the x-axis, 0 on the x-axis and > 0 above the x-axis

The graph crosses the x-axis at x = - 2 and x = 4 but cannot equal these values.

Hence f(x) < 0 in the interval - 2 < x < 4 → (1)