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Let fa(x) = with a E R

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Let fa(x) = with a E R. ax2 - 2ax + 1 (a) Find all the values of a for which the function fa(x) has a vertical
asymptote at x = 1. (b) Find all the values of a for which the function fa(x) has a horizontal asymptote at y = 1.
(c) Find all the values of a for which the function fa(x) is continuous everywhere.