Expression for a bounded function I have a bounded function,

$$
y=
    \begin{cases}
        1 &amp; \text{if $x&gt;1$} \\
        x &amp; \text{if $0\leq x\leq 1$}\\
        0 &amp;\text{if $x &lt; 0$}
    \end{cases}
$$
Does anyone know any simple math function to represent $y$? (not using a piece-wise function)

For example, Heaviside function is a similar approach.

Thanks
Let $H$ denote the unit step function.

$xH(x)$ is zero when $x$ is negative and equal to $x$ when $x$ is positive. $xH(x-1)$ is zero when $x$ is less than 1 and equal to $x$ otherwise. If I'm not mistaken, $$xH(x) - (x-1)H(x-1)$$ is the function you want.
$$
\int \rm rect\left( x- \frac12\right)\rm dx,
$$
but be careful when choosing $\rm{const}$...