Given the function f (x) = x3 + 2x2 - 3x - 5, what is the resulting function when f (x) is shifted to the right 1 unit? f (x + 1) = x3 + 5x2 + 4x - 5 f (x) + 1 = x3 + 2x2 - 3x - 4 f (x) - 1 = x3 + 2x2 - 3x - 6 f (x - 1) = x3 - x2 - 4x - 1

When a function is shifted to the right by 1 unit it is moved towards the negative side so we would be adding - 1 to the value of x. The function f (x) would be f (x-1). To determine the resulting function, we substitute to the parent function (x-1) to x. We do as follows:

f (x) = x^3 + 2x^2 - 3x - 5

f (x-1) = (x-1) ^3 + 2 (x-1) ^2 - 3 (x-1) - 5

f (x-1) = x^3 - 3x^2 + 3x - 1 + 2 (x^2 - 2x + 1) - 3x + 3 - 5

f (x-1) = x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5

f (x-1) = x^3 - x^2 - 4x - 1

Therefore, the correct answer is the last option.