Question

given the function f(x)=x^3 +x^2-2x+1 what is the resulting function f(x) is shifted to the left one unit

Answer 1

The resulting function is
`f(x+1) = x^3 + 4x^2 + 3x + 1`

Explanation:

Suppose we have a function f(x). If we want to shift the function 1 unit to the left, we find f(x+1).

In this question, we have:

`f(x) = x^3 + x^2 - 2x + 1`

Shifting 1 unit to the left:

`f(x+1) = (x+1)^3 + (x+1)^2 - 2(x+1) + 1`

`f(x+1) = (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2x - 2 + 1`

`f(x+1) = x^3 + (3+1)x^2 + (3+2-2)x + 1 + 1 - 2 + 1`

`f(x+1) = x^3 + 4x^2 + 3x + 1`

The resulting function is
`f(x+1) = x^3 + 4x^2 + 3x + 1`