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.

Explore the 3D plot of the function f(x, y) = x^2 + y^2, a classic example of a parabolic bowl in multivariable calculus. Understand how the surface rises as x and y increase and analyze the level curves for this function. Suitable for high school students in Grades 11-12 studying functions of two variables.

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