Math 115H (Assignments)

# Homework on 18 September 2017:

[Not to be turned in]

1. In class, we talked more about how to use $x$- and $y$-traces to understand the graph of a function $f\colon\R^2\to\R$.

Use these techniques to sketch the graphs of the following:

1. $f(x,y) = 1-x^2-y^2$
2. $f(x,y) = (xy)^3$
3. $f(x,y) = x + y$
2. In class, we discussed how a level set is the collection of points in the domain that cause a function to produce a specific (fixed) output.

Consider the function $f(x,y)=xy$ that we graphed in class today.

1. Sketch the level set for $f$ that produces the value $0$?
2. Sketch the level set for $f$ that produces the value $1$?
3. Sketch the level set for $f$ that produces the value $-1$?
3. Finish the WeBWorK assignment.

 Math 115H (Fall 2017) web pages Created: 18 Sep 2017 Last modified: Sep 18, 2017 2:18:46 PM Comments to: dpvc@union.edu