surface example

3D Cubic Surface Graph

A cubic sheet tilted by the y term.

z = x^3 - y

Quick facts

  • Formula: z = x^3 - y
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The x direction bends strongly while the y direction shifts height linearly.

Where it appears in calculus

Use it to show mixed polynomial behavior.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. 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 page

Teacher prompt

Question: Which direction has cubic growth?

Answer: The x direction has cubic growth.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Log Bowl

z = log(1 + x^2 + y^2)

A bowl that rises slowly as it moves outward.

Square Root Dome

z = sqrt(max(0, 16 - x^2 - y^2))

The upper half of a sphere-like dome.

Hyperbolic Valley

z = x*y

A saddle-like surface formed by multiplying x and y.

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.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners