Here's the 3D plot of the function $f(x, y) = x^2 + y^2$. This surface plot shows how the function increases as both $x$ and $y$ move away from zero, forming a parabolic bowl shape.

Would you like more details or have any questions?

Here are some additional questions to explore:

1. How would the plot change if the function was $f(x, y) = x^2 - y^2$?
2. What are the level curves for this function, and how can they be visualized?
3. How does changing the range of $x$ and $y$ affect the shape of the plot?
4. How would this function behave if we add a constant, making it $f(x, y) = x^2 + y^2 + c$?
5. What would the plot look like if the function were $f(x, y) = \sqrt{x^2 + y^2}$?

Tip: To understand the shape of a function like $f(x, y) = x^2 + y^2$, analyzing its level curves or contour plot in addition to the 3D plot can be helpful.