Question

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?

Answer 1

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