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Some hints: use the definition: f is a function iff a = b implies f(a) =...

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Advance Math

Some hints: use the definition: f is a function iff a = bimplies f(a) = f(b) and recall that in informal proofs we show animplication by assuming the if part of the implication, and thendeducing the then part of the implication.

The base case will show that a = b implies f(a) = f(b) when f(x)= c0 (a constant function). The inductive case willassume a = b implies f(a) = f(b) for degree k, and will deduce itis also true for degree k+1.

  1. Show that every polynomial of degree n:
    y = f(x) = cnxn +cn-1xn-1 + . . . + c2x2+ c1x + c0
    is a function by mathematical induction on degree n.
    Assume n is a nonnegative integer, all cis are real,cn ? 0, and x and y are also real.

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