The graph of the function g(x) is a translation of the graph of f (x) = x³. Graph the function g(x) = (x - 5)³ - 2.

Question

Quizplus · Accepted Answer

To translate a function by a certain amount, we need to subtract that amount from the input (x) value. So, to translate f(x) by 5 units to the right, we need to replace x with (x - 5). Similarly, to translate f(x) down by 2 units, we need to subtract 2 from the output (y) value. So, the function g(x) = (x - 5)³ - 2 represents a translation of f(x) by 5 units to the right and 2 units down. The graph of g(x) will be identical to the graph of f(x), except that it will be shifted 5 units to the right and 2 units down. The correct graph is shown in choice B.

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