Question

Given the function f(x) = x^3+2x^2-3x-5, what is resulting function when f(x) is shifted to the right 1 unit.

Answer 1

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

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