Searching function starting exactly constant and approaching another constant

for the default of an R API parameter i seek a function that has the property of yielding a good guess.

• I want the function to be defined for $\mathbb Z^+$ (But no reason not to define it for $\mathbb R^+$, i guess)


• I want it to be smooth



• It should satisfy both

  
  
  
  

  $$\mathrm f(x_{small}) = 1 \forall x_{small} \in \left(0, k\right]$$
  $$\lim_{x \rightarrow \infty} \mathrm f(x) = l$$

edit to be clear: $k$ and $l$ should be constants appearing in the function definition.

E.g. with $k = 1000$ and $l = 0$, the $f(x) = 1 \forall x \in (0, 1000]$. Then it should gradually decline and approach 0.

To simplify, the function can be written as:

$$
\mathrm f(x) = \begin{cases}
1 & \text{if } x \le k \\
[\dots] & \text{otherwise}
\end{cases}
$$