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Stitz-Zeager_College_Algebra_e-book

# A y 4 1 x 1 7 1 y 7 x 29 7 b y 3 2x 0 y

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Unformatted text preview: ant line through these points. For that reason, some textbooks use the notation msec for the average rate of change of a function. Note that for a linear function m = msec , or in other words, its rate of change over an interval is the same as its average rate of change. 2.1 Linear Functions 121 y = f (x) (b, f (b)) (a, f (a)) The graph of y = f (x) and its secant line through (a, f (a)) and (b, f (b)) The interested reader may question the adjective ‘average’ in the phrase ‘average rate of change.’ In the ﬁgure above, we can see that the function changes wildly on [a, b], yet the slope of the secant line only captures a snapshot of the action at a and b. This situation is entirely analogous to the average speed on a trip. Suppose it takes you 2 hours to travel 100 miles. Your average speed is 100 miles = 50 miles per hour. However, it is entirely possible that at the start of your journey, you 2 hours traveled 25 miles per hour, then sped up to 65 miles per hour, and so forth. The average rat...
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