Elementary function that $f(0)=1$ and $f(x)=0$ for all $x>0$.

Question

Here is a short question: finding a function that 1) $f(0)=1$ and 2) $f(x)=0$ for all $x>0$.

I have two functions in mind:

1. Something like Dirac delta: $\delta_0(x)$.
2. Something like $f(x)=1-\text{sign}(x)$.

But they are (arguably) not elementary. A function that is simpler and more elementary will be appreciated!

Answer 1

You can take the example

$$f(x)=\lfloor e^{-x} \rfloor$$

So

$$f(0)=\lfloor 1\rfloor=1$$ and for $ x>0$

$$0<e^{-x}<1\implies f(x)=0$$