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

Explanation:

Step1: Check first table

For the first table, when (x) goes from (-2) to (-1) (in the interval ((-2,0))), (f(x)) goes from (0) to (- 5) (decreases), and when (x) goes from (-1) to (0), (f(x)) goes from (-5) to (0) (increases). So it is not decreasing over ((-2,0))

Step2: Check second table

The second - table does not have (x) values in the interval ((-2,0)) other than the endpoints. So we can't determine if it is decreasing over ((-2,0))

Step3: Check third table

For the third table, when (x=-2), (f(x) = 0), when (x=-1), (f(x)=-10), and when (x = 0), (f(x)=-24). As (x) increases from (-2) to (0) (in the interval ((-2,0))), (f(x)) decreases.

Answer:

The third table.