I was trying to find range of the function :
$$f(x)=\frac{x^2-3x+2}{x^2+2x-3}$$
we have the Domain as:
$$D_f=\mathbb{R}-\left\{-3,1\right\}$$
We have $$y=f(x)=\frac{(x-1)(x-2)}{(x+3)(x-1)}=\frac{x-2}{x+3}\tag{1}$$
So we get:
$$x=\frac{3y+2}{1-y}$$
so $y \ne 1$ Also when $x=1$ in Equation $(1)$ we get $y=\frac{-1}{4}$
Since $x=1$ is not in domain we exclude $y=\frac{-1}{4}$ in range.
hence range is $$D_r=\mathbb{R}-\left\{1,\frac{-1}{4}\right\}$$
But when I draw the graph of $$f(x)=\frac{x^2-3x+2}{x^2+2x-3}$$ in Desmos, why the value $\frac{-1}{4}$ is not excluded in range?