Math 115H (Assignments)

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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

Assignments