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Easy: Linear functions
The average rate of change from x = p to x = q is the change in the function divided by the change in x: (f(q) − f(p)) / (q − p). For a line it's the slope everywhere; for curves it depends on the interval.
Find the average rate of change over the interval.
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It is the slope of the line through two points on the graph: (f(b) − f(a))/(b − a). For a linear function it is the same for every interval.
Its graph curves, so the line between two points gets steeper or flatter depending on where you measure. For f(x) = x², it is 1 from 0 to 1 but 5 from 2 to 3.
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