## Tutoring on Introduction to Functions of Several Variables

Learning Objectives:

#### Understand and Apply Functions of Several Variables.

Math Tutoring on Introduction to Functions of Several Variables

A function  is a function of two variables.

Domain and Range:

The Domain is the set of all possible values of ‘x’ and ‘y’. (set of inputs)

The Range is the set of all possible values of ‘z’ from the Domain. (set of outputs)

The Graph is the set of all possible points (x, y, z) produced by the function in math tutoring. Geometrically, the Graph is a surface in space.

Level Curve:

Level Curves or Contour Lines are another way to represent a function .

By letting ‘z’ equal to some constant ‘c’, we obtain a single Level Curve. If we do this for several values of ‘c’, we have a set of Level Curves to represent a function. Some real life examples of Level Curves are Pressure Map, Temperature Map, and Altitude Map etc.

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Hook Questions:

1.   What is the Domain and Range of functions of two variables?

2.   What is Level Curve? Give some real life examples of Level Curves?

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