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 x - 20
O x ≥ 3

Answer 1

The domain of the shifted function
`\(g(x) = 4√(x) - 3\)` is
`\(x \geq 3\).`

To find the domain of the shifted function
`\(g(x) = 4√(x) - 3\)`, we start with the original domain of
`\(f(x) = 4√(x)\)`, which is
`\(x \geq 0\)`. The square root function is defined only for non-negative values.

Now, for the shifted function g(x), subtracting 3 from the function doesn't affect the domain. The square root of a non-negative number minus 3 is still well-defined. Therefore, the domain remains
`\(x \geq 0\).`

Among the given options,
`\(x \geq 3\)` is equivalent to
`\(x \geq 0\)` when considering the shift down by three units. Hence, the correct choice for the domain is
`\(x \geq 3\).`

The final answer is
`\( \boxed{\text{O } x \geq 3} \).`