calculus - A function with certain shape

I'm trying to simulate a certain type of condition with a continuous and twice differentiable function $f(x)$ that has the following shape:

1. The limit of $f(x)$ at $-\infty$ is finite but less or equal to zero, i.e.
   $$-\infty < \lim_{x \to -\infty}f(x) \leq 0$$


2. There exists a unique point $y \in \mathbb{R}$ such that $f(x)$ is decreasing on $(-\infty,y)$ and increasing on $(y,\infty)$.


3. The limit at $\infty$ is positive or infinity i.e. $$0<\lim_{x \to \infty} f(x) \leq \infty.$$

However I'm struggling to find a good example of such a function that is simple enough to make the point clear. In other words I'm looking for a explicit examples of a function with the properties that I described above.

Answer

Here's one that will work:

$$f(x)=\begin{cases}-e^{-x^2},\;&x<0 \\ 1-2e^{-x^2/2},\;&x\ge 0. \end{cases}$$
Here's a plot:

Here's another that might work (inspired by David G. Stork's answer):

$$f(x)=\operatorname{tanh}(x)-e^{-x^2/4}.$$
Plot:

The thing is, I haven't double-checked that this function is monotonically decreasing before some $x,$ and monotonically increasing after.