Answer
The line $ y=0$ ($ x $-axis) is the horizontal asymptote of the given function.
Work Step by Step
To find the horizontal asymptotes, we calculate the following limit
\begin{align*}
\lim _{t \rightarrow \infty}\frac{3^t}{1+3^{-t}}
&=\frac{\infty}{ 1+0}=\infty.
\end{align*}
\begin{align*}
\lim _{t \rightarrow -\infty}\frac{3^t}{1+3^{-t}}&=\lim _{t \rightarrow -\infty}\frac{1}{3^t+3^{-t}}\\
&=\frac{1}{ \infty+0}=0.
\end{align*}
Hence, the line $ y=0$ ($ x $-axis) is the horizontal asymptote of the given function.
