The graph of f(x) shown below has the same shape as the graph of g (x) = x^3 - x^2 but it is shifted to the left 1 unit what is the equation

f(x) = (x + 1)³ - (x + 1)² = x³ + 2 x² + x

Step-by-step explanation:

To shift g(x) to the left by one unit, replace all x in the expression of g(x) with (x + 1). How does this work? For example, g(x) = -2 for x = -1 in this question. f(x) = g(x + 1) may also equate -2, but only one unit to the left of x = -1 at x = -2 since -2 + 1 = -1. So is the case for the rest of the points on g(x). f(x) = g(x + 1) leads to the same set of values but only at one unit to the left. Adding one to the independent variable of g(x) shifts the graph to the left by one unit.

To find g(x + 1), replace every x in the equation x³ - x² with (x + 1):

f(x) = g(x + 1) = (x + 1)³ - (x + 1)².

Expand (x + 1)³ - (x + 1)² using the binomial theorem:

f(x) =  (x + 1)³ - (x + 1)² = x³ + 3 x² + 3 x + 1 - (x² + 2 x + 1) = x³ + 2 x² + x

what is the question?

step-by-step explanation: