Notations for multiple linear equations on Cartesian coordinate system

Question

Lets say I have $2$ linear equations, $y = x$ and $y = 2x$. However, $y = x$ is only applicable for $x$'s from $0$ up to $4$, and $y = 2x$ is only applicable for $x$'s from $4$ to infinity. How do I write this mathematically?

Answer 1

You can write this as$$y=\cases{x,0\le x\lt4\\2x,4\le x}$$ You can also use the Heaviside function $$H(x)=\cases{0,x\lt0\\1,x\ge1}$$ $$y=xH(x)(1+H(x-4))$$