# Can you graph a multivariable function?

## Can you graph a multivariable function?

Whenever you’re dealing with a multivariable function, the graph of that function will be a three-dimensional figure in space. Then we want to be able to transfer all those two-dimensional curves into the two-dimensional plane, sketching those in the xy-plane.

## How do you plot two variables on a graph?

Graph a linear equation by plotting points.

1. Find three points whose coordinates are solutions to the equation. Organize them in a table.
2. Plot the points in a rectangular coordinate system. Check that the points line up.
3. Draw the line through the three points.

What is the graph of a multivariable function?

The graph of a function f of two variables is the set of all points (x,y,f(x,y)) where (x,y) is in the domain of f . This creates a surface in space. 12.1: Introduction to Multivariable Functions – Mathematics LibreTexts

How to sketch level curves of multivariable functions?

What we want to be able to do is slice through the figure at all different heights in order to get what we call the “level curves” of a function. Then we want to be able to transfer all those two-dimensional curves into the two-dimensional plane, sketching those in the xy-plane. This will give us the sketch of level curves of the function.

### Which is an example of a multidimensional graph?

Examples and limitations of graphing multivariable functions. Graphing a function with a two-dimensional input and a one-dimensional output requires plotting points in three-dimensional space. This ends up looking like a surface in three-dimensions, where the height of the surface above the -plane indicates the value of the function at each point.

### Can you graph a multidimensional function one slice at a time?

In this way, you can understand the three-dimensional graph of a multivariable function one slice at a time by holding one variable constant and looking at the resulting two-dimensional graph. You can also graph a function with a one-dimensional input and a two-dimensional outputâ€”although, for whatever reason, this is not commonly done.