Level Curves

Level Curves

So what is a level curve?...

Here are the level curves for the function f(x,y) = x^2 - y^2

Represent 3-D images on a 2-D sheet of paper!

Definition - The set of points in the plane where a function f(x,y) has a constant value f(x,y) = c is called a level curve of f.

Procedure:1. Set f(x,y) = c2. Choose values for c and graph the resulting curves on the x-y plane. (We usually like to use c = -2,-1,0,1, and 2).3. Label each curve with its corresponding c-value. The c-values represent the number of units above or below the x-y plane that the curve lies in space. So, imagine that your desk is the x-y plane. a curve whose c-value is 2 will lie 2 units above your desk. a curve with a c-value of -3 will lie 3 units below your desk. A c-value of 0 means the curve is on your desk.4. Look at the picture and try to visualize what the graph would look like!

Below is an awesome video that explains step-by-step how to sketch level curves, and then even compares the resulting curves with the actual 3-D graph of the function! Turn your volume up though, it is really quiet.

Still sort of confused?