Algebra 18 - Multivariable Functions

The video introduces functions, starting with single input functions and their domains and ranges. It then progresses to multivariable functions, explaining how they map multiple inputs to outputs using Cartesian products. The video also discusses applications in physics and engineering, such as representing air temperature in a room with three variables.

What is the primary difference between single-variable functions and multivariable functions?

Explain the concept of domain and range in the context of functions.

How do you represent a function of two real variables?

What is the Cartesian product and how is it used in defining the domain of a function with two input variables?

Describe how the graph of a function of two variables differs from that of a function of one variable.

What does it mean for a function to map points in a plane to points on a line?

In what scenarios might functions of three or more variables be encountered?