martingoodly martingoodly

01-05-2018
Mathematics

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Given the function f(x) = x^3 + x^2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

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sqdancefan sqdancefan

02-05-2018

The resulting function g(x) is ...
g(x) = f(x +1)
g(x) = (((x +1) +1)(x +1) -2)(x +1) +1
= ((x +2)(x +1) -2)(x +1) +1
= (x² +3x)(x +1) +1
= x³ +4x² +3x +1

The shifted function g(x) is ...
g(x) = x³ +4x² +3x +1

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