Which of the following is true for the identity function $f\left(x\right)=x$?

Its graph is a parabola opening upward with vertex at the origin

Its graph is a line through the origin with slope $1$, domain $(-\infty ,\infty )$, and range $(-\infty ,\infty )$

Its graph is a horizontal line $y=c$ for some constant $c$

Its graph is defined only for nonnegative $x$ and $y$