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?

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