Why does the graph of $\sqrt{x}+\sqrt{y}=1$ not touch either of the axes?

Question

I entered this function on a graphing calculator and found that it did not touch either axes. Can someone please explain why x,y cannot be zero?

Answer 1

Your equation translates to $ \sqrt{y} = 1-\sqrt{x} $ and $ y=(1-\sqrt{x})^2 $ for $x>0$

Now try to solve your equation for $y=0$ : $$0=(1-\sqrt{x})^2 $$ $$0=1-\sqrt{x} $$ $$1 = \sqrt{x} $$ $$x=1$$ and vice versa. So you have to points $(0|1)$ and $(1|0)$ touching the axes.

Answer 2

Here's the graph. Of course the function goes through both $(0,1)$ and $(1,0)$:

Answer 3

Which graphics calculator are you using I plotted it using Desmos and it touches the axis at points $(0,1)$ and $(1,0)$