Question

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

Answer 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.