Algebra - Functions

Define $\{x\} = x-\lfloor x \rfloor$. That is to say, $\{x\}$ is the "fractional part" of $x$. For example, if you were to expand a positive number  as a decimal, $\{x\}$ is the stuff after the decimal point. For example $\left\{\frac{3}{2}\right\} = 0.5$ and $\{\pi\} = 0.14159\dots$

Now, using the above definition, determine if the function below is increasing, decreasing, even, odd, and/or invertible on its natural domain:

$f(x) = \lfloor x \rfloor - \left\{ x \right\}$

For each property, write inCreasing, Decreasing, Even, Odd, inVertible in that order (alphabetical).