Question

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

Answer 1

When the function is asked to be shifted to 1 unit to the left, we replace x with x + 1. Hence, f(x) = x3 + 2x2 - 2x + 1; f(x + 1) = (x + 1)^3 + (x + 1)^2 - 2(x + 1) - 5
= (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2(x + 1) + 1 = x^3 + 3x^2 + x^2 + 3x + 2x - 2x + 1 + 1 - 2 + 1 = x^3 + 4x^2 + 3x + 1

The final equation is x^3 + 4x^2 + 3x + 1

Answer 2

we have

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

we know that

if f(x) is shifted to the left
`1` unit

then

the rule of the translation is

`f(x)-------> g(x)`

`(x,y)-------> (x-1,y)`

the resulting function will be

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

using a graphing tool

see the attached figure to better understand the problem

therefore

the answer is

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