Will $y=\sqrt x$ be an into function or onto function? Will R $f(x)=\sqrt x$ be an into function or onto function? How to understand from the graph that it will be onto or into function (just by looking at the graph) ?
Domain:positive real numbers
Range:all real numbers

No, the square root function is not surjective as a function $\sqrt\cdot:\Bbb R^+\to\Bbb R$, because the square root of a positive real number is positive real; hence $\sqrt x=-1$ has no solution. It is "into", because the square root always gives real numbers for positive real input.
Generally, a function $f:A\to\Bbb R$ is onto if it touches every horizontal line; in this case it misses any line below the $x$-axis, so it is not onto.
