So I'm trying to make my own implicit equation and plot it using desmos.com (cant link because of rep)
Everything is fine, I'm using this method:
$( y - f(x) ) ( y - g(x) ) .... = 0$
For example, if I plot
$(y-x^2)(y-x)=0$
it plots fine (both curevs).
However, if I add this 'factor': $(y+\sqrt{1-(x-2)^2}-2)$ everything get 'restricted' in a weird way. See this image:
https://i.stack.imgur.com/woVjq.png (all three factors)
https://i.stack.imgur.com/YgxKh.png (without the troubling factor)
Why is this happening? How can I fix it?
The third factor only takes values between $1 \geq x \geq 3$. Therefore, the entire function's domain is restricted to that area. This is because:
$\sqrt{1-(x-2)^2}$ means that $1-(x-2)^2 \geq 0$, leading to $1 \geq (x-2)^2$
Take the square root of both sides to get:
$$1 \geq \left| (x-2) \right|$$ $$-1 \leq x-2 \leq 1$$
So $x$ can only be in the domain:
$$1 \leq x \leq 3$$
If there isn't any reason why not, I suggest that you enter the factors separately and set them all to 0, as this will yield the same graph, and according to my tests, does work.
If you are unclear about why they would yield the same graph, it is because, for your equation to equal zero, one of the factors must equal zero and, conversely, if one of your factors equals zero, then your entire equation does as well.
Therefore, you would enter your equations as such:
$$(y-x^2)=0$$ $$(y-x)=0$$ $$(y-\sqrt{1-(x-2)^2}-2 = 0$$