Problem Three: 2000-2001

 Calculus I (AB) and II (BC): Continuity, Schmontinuity
Give the value of M, in terms of a, b, and c, which makes the function f(x) continuous if
Difficulty Rating:

Solution:
The rule which defines this function changes at x1. If the function is to be continuous, the two pieces of the graph must meet there. Thus, both functions must have the same output (height) when x1. Plug in x1 and solve for M:
Substituting this ugly fraction for M results in a value of a b + c for both pieces of the function when x1.

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