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Examine two ways a line changes:

  1. Sketch . What are ? How are the function values changing as increases?

    Increasing line, passing through the points (0, comma 1) & (2, comma 9).

    Compute the finite differences (that is, find the difference in -values as increases) and look for a pattern.

  2. Calculate the area under the curve for if . How is the area changing as increases?

    Use geometry to find the area of the trapezoid between and for each value of . Keep your results organized.

    Is the difference between the areas growing constantly or linearly? If not, how else could it be growing, and by what pattern each time?