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.

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By scrutinizing the graph, it is evident that the function f(x) is negative in the interval -2 < x < 4. This conclusion is drawn from observing where the graph resides below the horizontal axis, providing a clear understanding of the intervals where f(x) exhibits a negative value.

The correct answer is option 1.

To determine the intervals where the given function f(x) is negative, the correct option is identified as -2 < x < 4. The process involves examining the graph of the function to discern where it lies below the horizontal axis, indicating a negative value.

By visually inspecting the graph, it becomes apparent that f(x) is negative in the interval (-2, 4). It's crucial to note the use of an open interval, implying that f(x) is strictly less than 0, not equal to 0.

The derived interval expression is -2 < x < 4, signifying that the function f(x) is negative for values of x within this range. The open interval emphasizes the exclusion of the boundary points where f(x) equals 0.

Therefore, from the given options the correct one is 1.

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