Which of the following families of real functions are algebras of functions? (For each, either show it is an algebra of functions, or else identify a necessary property that is not satisfied.) i. Polynomials of degree at most 2. (That is, polynomials of the form ax2 +bx+c, where any or all of a, b, c may be 0.) ii. Functions f such that f(x) ≤ 6. iii. Functions f that are everywhere defined, and that are continuous at the point c = 2.

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