examining intervals in a table of values\nwhich table shows a function that is decreasing over the interval…

Explanation:

Step1: Check first table

In the first table, when (x) goes from (-2) to (-1) (within the interval ((-2,0))), (f(x)) goes from (0) to (- 5), and when (x) goes from (-1) to (0), (f(x)) goes from (-5) to (0). It is not decreasing over the whole interval ((-2,0)) as it first decreases then increases.

Step2: Check second table

In the second table, the (x) - values (-2) and (0) are in the set but we need to check the values within the open - interval ((-2,0)). There are no (x) values in the interval ((-2,0)) in this table, so we can't determine the behavior of the function on ((-2,0)) from this table.

Step3: Check third table

In the third table, when (x=-2), (f(x) = 0), when (x=-1), (f(x)=-10). As (x) increases from (-2) to (-1) (within the interval ((-2,0))), (f(x)) decreases. So the function is decreasing over the interval ((-2,0)) in this table.

Answer:

The third table.