Graph of the $\sqrt { x } $ Why does the graph only go to the right and up? Wouldn't there be negative values of y as well? Since, for example, the $\sqrt{4}$ is $2$ and $-2$

A function $f$ is a map $f: X\rightarrow Y$ which for every input $x\in X$ gives precisely one output $f(x)\in Y$. Taking $\sqrt4=\pm2$ is not a function, because it has two outputs.
The notation $\sqrt{x}$ is used to denote the function $\sqrt{\:\:\:}\:: \mathbb{R}^{+}\rightarrow\mathbb{R}^{+}$ with positive image, ignoring the negative numbers which are square roots. When you graph $\sqrt{x}$, you are graphing this function.
