k is a constant and the values in the table are x= -6,-3,0,3,6 and the f(x)= 5,k,2,4,5.find the value of k such that the average rate of change over the interval -3<=x<=3 equals 1.

Answer 1

The ordered pairs that go with the interval -3 < x < 3 are: (-3, k) and (3, 4) therefore the slope between these points can be calculated using the slope formula:

So, since m = 1 (as we are told) then:

(4 - k)/(3 - -3) = 1

(4 - k)/6 = 1

(4 - k) = 6

4 - 6 = k

k = -2