The graph of the function g(x) is a translation of the graph of f (x) = x³. Graph the function g(x) = (x - 3)³ - 1.

Question

Quizplus · Accepted Answer

We know that a translation of x units to the right corresponds to adding x to the input of the function, while a translation of y units upwards corresponds to adding y to the output of the function. In this case, g(x) = (x - 3)³ - 1 is a translation of f(x) = x³ to the right by 3 units and downwards by 1 unit. So the graph of g(x) will be the same as the graph of f(x) but shifted 3 units to the right and 1 unit downwards. Looking at the graphs given, we can see that only graph (B) has been shifted to the right by 3 units and downwards by 1 unit. Hence, the answer is B.

The Graph of the Function G(x) Is a Translation of the Graph