Question

The graph of the function f(x) = 4√x is shifted down by three units.

What is the domain of the resulting function?
O X² ≥ 12
O x² ≥ 3
O x² ≥ 0
O x≥ 3

Answer 1

The domain of the function after being shifted down by three units remains the same as the original function, which is all non-negative real numbers (x ≥ 0).

Step-by-step explanation:

The student is inquiring about the domain of a transformed square root function. Specifically, the function f(x) = 4√x has been shifted downward by three units, resulting in a new function g(x) = 4√x - 3. The domain of the original function f(x) is all non-negative real numbers (x ≥ 0) because the square root is not defined for negative numbers.

The transformation does not alter the domain since shifting a graph vertically does not affect the input values for which the function is defined. Therefore, the domain of the new function g(x) is also all non-negative real numbers, which corresponds to the expression x ≥ 0.