Select the statement that best describes the end behavior of the function \( h(x)=\sqrt[3]{x-4}+\frac{1}{3} \). Statement \#1: As \( x \) approaches infinity, \( y \) approaches negative infinity. Statement \#2: As \( x \) approaches negative infinity, \( y \) approaches infinity. Statement \#3: As \( x \) approaches infinity, \( y \) approaches infinity. (1 point)

The function \( h(x) = \sqrt[3]{x-4} + \frac{1}{3} \) is a cubic root function, which means it has a characteristic end behavior. As \( x \) approaches infinity, the term \( \sqrt[3]{x-4} \) also approaches infinity, thus making \( h(x) \) approach infinity as well (Statement #3). Conversely, as \( x \) approaches negative infinity, \( \sqrt[3]{x-4} \) approaches negative infinity, which means \( h(x) \) does as well. In simpler terms, if you were to sketch \( h(x) \), you'd see it rising to the right and dropping to the left, displaying the signature S-shape of cubic functions! Keep in mind, the transformations do not change the general trend; it just shifts the entire function slightly. So, for good old end behavior, Statement #3 is your best buddy!