1. The problem is to recreate the image of two hands nearly touching using equations suitable for Desmos, specifying each equation with its domain and range to correctly position the parts. 2. We start by approximating parts of each hand with simple curve equations such as circles, ellipses, and polynomial or parametric curves. 3. For the left hand (approximate coordinates focusing on the negative x side): - Palm: Use an ellipse centered at approximately $(-4,-0.5)$ with semi-major axis 3 and semi-minor axis 2: $$\frac{(x+4)^2}{9} + \frac{(y+0.5)^2}{4} = 1,$$ domain: $x \in [-7,-1]$, range: $y \in [-2.5,1.5]$. - Fingers: Approximate each finger with vertical or slightly curved lines or quarter circles. For example, the index finger could be a quarter circle: $$ (x+1.5)^2 + (y-1.5)^2 = 0.5^2,$$ domain: $x \in [-2,-1],$ range: $y \in [1,2]$. 4. For the right hand (positive x side): - Palm: Another ellipse centered near $(4,-0.5)$ with axes similar to the left: $$\frac{(x-4)^2}{9} + \frac{(y+0.5)^2}{4} = 1,$$ domain: $x \in [1,7]$, range: $y \in [-2.5,1.5]$. - Fingers reach left, similarly approximated by quarter circles or bezier-like curves. For example, an index finger segment: $$ (x-1.5)^2 + (y-1.5)^2 = 0.5^2,$$ domain: $x \in [1,2],$ range: $y \in [1,2]$. 5. To approximate finger curves, add polynomial segments or parametric curves adjusting slope and curvature to create slight bends. 6. Summarizing, each hand is largely composed of elliptical equations for palms and circle arcs or polynomial segments for fingers, limited to domains and ranges so they appear on each respective side without overlap. 7. These domain restrictions make the drawing appear within the coordinate frame around $x \in [-7,7]$ and $y \in [-5,5]$. 8. In Desmos, entering these equations with their domain restrictions will plot the shapes approximating the hands nearly touching. Final note: specific approximations would require manual tweaking in Desmos for artistic detail, but ellipses and circles with proper positioning are a good base.