Final answer:
The end behavior of the given radical function “f(x) = 4 √x - 6” is that as x approaches infinity, the value of f(x) increases without bound, and there is no behavior as x approaches negative infinity since the function is undefined for x < 0.
Step-by-step explanation:
The end behavior of a function describes the behavior of the graph of the function as x approaches infinity or negative infinity.
For the radical function f(x) = 4 √x - 6, as x approaches infinity, the term 4 √x grows without bound, but at a slower rate compared to polynomial functions, since it's a square root.
Therefore, as x increases, f(x) will also increase without bound.
However, since the domain of the square root function only includes non-negative numbers, there is no behavior as x approaches negative infinity; the function is undefined for x < 0.