surface example
3D Hyperbolic Valley Graph
A saddle-like surface formed by multiplying x and y.
z = x*yQuick facts
- Formula: z = x*y
- Category: surface
- Tags: surface, calculus, z=f(x,y)
What this graph represents
The sign of z depends on whether x and y have matching signs.
Where it appears in calculus
It is a simple way to teach quadrants in 3D.
How to use this graph
- Rotate the surface by dragging with your mouse or finger
- Use the Embed button to copy an
<iframe>for your LMS or lesson page - Click PNG to export a classroom-ready image
- Click Formula or LaTeX to copy the equation for your notes
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageTeacher prompt
Question: Where is z positive?
Answer: z is positive when x and y have the same sign.
Related graphs
Explore more surface examples and compare shapes, slices, and contour behavior.
Cosine Hills
z = cos(x) + cos(y)A regular field of smooth hills and basins.
Egg Crate Surface
z = sin(x) * sin(y)A repeating grid of peaks and pits.
Radial Decay
z = 1 / (1 + x^2 + y^2)A smooth mound that decays toward zero.
Mexican Hat Surface
z = (1 - x^2 - y^2) * exp(-(x^2 + y^2) / 2)A central peak surrounded by a circular valley.
Ridge Surface
z = exp(-x^2)A ridge that is constant in the y direction.
Valley Surface
z = y^2 - 2*xA parabolic valley tilted along the x-axis.
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