Question

Given the function f(x) = x3 + x2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

Answer 1

`f(x) \xrightarrow{\hbox{1 unit to the left}} f(x+1) \\ \\ f(x)=x^3+x^2-2x+1 \\ \\ f(x+1)=(x+1)^3+(x+1)^2-2(x+1)+1= \\ =x^3+3x^2+3x+1+x^2+2x+1-2x-2+1= \\ =x^3+4x^2+3x+1`

The resulting function is:

`\boxed{y=x^3+4x^2+3x+1}`

Answer 2

For this case we have the following function:

`image`

We apply the following function transformation:

Horizontal translations:

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left.

We have then for h = 1:

`image`

Rewriting we have:

`image`

Rewriting we have:

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

Answer:

The resulting function when f (x) is shifted to the left 1 unit is:

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