Unformatted text preview: f & x ± & & & x & 2 ± 2 x & x ± 1 ± 2 & x ± 3 ±& x ± 4 ± . With a similar argument, a possible polynomial function for the second graph is g & x ± & & x & 2 ± x & x ± 1 ±& x ± 3 ±& x ± 4 ± . b. Assume that any exponential function a x (for a ´ 1) dominates (i.e. larger than) a power function x n ( n is an integer) for large x values (i.e. as x ² ± ). Use this to explain why any such exponential function dominates any polynomial function for large x values. Solution. We know that a polynomial function of degree n behaves like the power function x n for large x values. So, if a x (for a ´ 1) dominates x n for large x values, then it also dominates a polynomial function (of degree n ) as x ² ± ....
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 Spring '10
 Many
 Math, Exponential Function, Derivative, Exponentiation, Complex number, polynomial function

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