For all $x>0$, it is true that $2^{x}<2x+2$.

For all $x>0$, it is true that $2^{x}>2x+2$.

There is a constant $c$ such that if $0<x<c$, then $2^{x}<2x+2$, but if $x>c$, then $2^{x}>2x+2$.

There is a constant $c$ such that if $0<x<c$, then $2^{x}>2x+2$, but if $x>c$, then $2^{x}<2x+2$.