Question

F(x) = x²

g(x) =(x - 6)²

Complete the description of the transformation. Use nonnegative numbers.

To get the function g, shift f _______ by ____ units.

Answer 1

To get the function g from f(x), we must shift f(x) to the right by 6 units, since g(x) = (x - 6)².

Step-by-step explanation:

To understand the transformation required for function g(x) from function f(x), we look at the given expressions. The original function f(x) = x² has been modified to g(x) = (x - 6)². This indicates a horizontal shift of the graph of the function. In general, if we have a function f(x - d), this represents a translation of the function to the right by d units. Conversely, f(x + d) translates the function to the left by d units.

Hence, to transform f(x) into g(x), we shift f(x) to the right by 6 units. The transformation description should read as follows: To get the function g, shift f to the right by 6 units.