Consider the function $g(x) = 6 − 2x$.  

1. What is the average rate of change of g over the interval $2 ≤ x ≤ 6$?

   Hint (a):

   $\frac{g(6) - g(2)}{6-2}$

2. Does the average rate of change differ for the interval $5 ≤ x ≤ 7$? Why or why not?

   Hint (b):

   $\frac{g(7) - g(5)}{7-5}$

3. Prove your answer to part (b) by computing the average rate of change for $g$.

   Hint (c):

   $\frac{g(b) - g(a)}{b-a} = \frac{6 - 2b - (6 - 2a)}{b - a} =$