Can you explain how a table can be used to find the rate of change

A table will generally give you an output value for each of several input values. To find the average rate of change over some range of inputs, divide the difference between output values by the difference between input values for the corresponding inputs.

For example, consider the table

input output

.. 1 3

.. 3 -5

The average rate of change between these input values is

... (change in output)/(change in input) = (-5 -3)/(3 - 1) = -8/2 = -4.