Section 3.2 Level Curves
As we have seen, visualising the surface corresponding to the function
Definition 3.2.2.
The level curves of a functionEach point in the domain of the function lies on exactly one level curve.
When a collection of level curves for a function are drawn on the same plane it is sometimes called a contour plot.
We can also think of level curves as the intersection of the surface and the horizontal plane
Example 3.2.3.
Draw the level curves associated with
The level curves of a function satisfy the equation
Thus the level curves are rectangular hyperbolae (except for

Example 3.2.5.
Draw a contour plot for the function
The contours (i.e. level curves) of a function satisfy the equation
that is, circles centred on the origin and whose radius is

Exercises Example Tasks
1.
Draw the level curves associated with
2.
Make a rough sketch of the contour map (centred on the origin) for the function whose graph is:

3.
Make a rough sketch of the contour map (centred on the origin) for the function whose graph is:
