How to graph a functions without using calculus?

Question

How to graph function: $$ y=\frac{6 \sqrt x}{\sqrt x+2}$$ without using calculus?

I wanted to use transformations to graph but I did not know where to start.

Answer 1

If you have to do it truly by hand, probably the easiest is to write $$y=6-\frac {12}{\sqrt x + 2}$$ which makes it clear there is a horizontal asymptote at $6$. You need $x \ge 0$ for the square roots to make sense, so plug in numbers that are easy to take the square root of, like $0,1,4,9,16$ for $x$ and plot the points. You might even do $x=\frac 14$ because that is easy to take the square root of. You will get something like this from Alpha