1) not sure of an example but it will be something with exponential growth.
2) Constant rate of change means the slope is the same between every point (always represented by a straight line). Average rate of change is the slope between the first and last point (not usually represented by a straight line).
3) g(x) = 3(2ˣ) - 6
g(0) = 3(2°) - 6 = 3(1) - 6 = 3 - 6 = -3 ⇒ coordinate (0, -3)
g(3) = 3(2³) - 6 = 3(8) - 6 = 24 - 6 = 18 ⇒ coordinate (3, 18)
average rate of change (slope) from x = 0 to x = 3: [tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{18 - (-3)}{3 - 0}[/tex]
= [tex]\frac{21}{3}[/tex]
= 7
