The end behavior of the logarithmic function f(x) = log3(x) demonstrates that as x approaches infinity, the function f(x) also approaches infinity. In other words, the graph of the function continues to rise slowly, but without bound, as you move to the right along the x-axis.
Conversely, as x approaches zero from the positive side, f(x) approaches negative infinity. This reflects the characteristic of logarithmic functions where they are undefined for x ≤ 0, but they trend downwards significantly as they approach the x-axis from the right.
Thus, the correct statement would be: the logarithmic function increases without bound as x increases and decreases without bound as x approaches zero from the right.