Textbook Problem

(a) What is a function of two variables?

(b) Describe three methods for visualizing a function of two variables.

To determine

To state: The function of two variables.

Explanation of Solution

Let the function be $f\left(x,y\right)$.

The function of two variables is assigned by a two real numbers in ${ℝ}^2$ that should be inside the domain region.

Thus, the result obtained is a real number for the region $\left\{f\left(x,y\right)|\left(x,y\right)\in D\right\}$.

To determine

To describe: The three methods to visualize the function of two variables.

Explanation of Solution

Statement:

Let the function be $f\left(x,y\right)$.

The methods for the function to observe the result is by using graph, vector diagram and level curves.