To find the range of the radical function f(x) = sqrt(x) - 2 + 4, we first need to consider the domain of the function. Since we're taking the square root of x, the domain must be x ≥ 0 to ensure that the square root is defined.
Now, let's find the range. We can start by finding the minimum value of f(x). The minimum value of sqrt(x) occurs when x = 0, and then we subtract 2 and add 4:
f(0) = sqrt(0) - 2 + 4 = -2 + 4 = 2
Next, let's consider what happens to f(x) as x increases without bound. As x gets larger and larger, sqrt(x) increases without bound, and the rest of the function (subtracting 2 and adding 4) shifts this upwards. Therefore, the range of f(x) is all real numbers greater than or equal to 2.
In interval notation, the range is [2, ∞).
