Functions with multiple variables

Thread starter Niles
Start date Sep 29, 2007
Tags

Functions Multiple Multiple variables Variables

In summary, a function with multiple variables is a mathematical relationship between two or more variables, represented as f(x, y) or f(x, y, z). To graph it, a three-dimensional coordinate system is needed. The difference between a function with one variable and multiple variables is that the latter takes in multiple values and produces a single output. To find the domain and range, the function can be graphed or solved algebraically. Additionally, a function with multiple variables can be optimized by finding the maximum or minimum values through taking partial derivatives and solving for the variables.

Sep 29, 2007

Niles

Homework Statement

I have a function f(x,y,z) = 1/(x^2+y^2+z^2). I have to find the domain.
It is R^3, but x^2+y^2+z^2 != 0. How do I write that and am I correct?

Physics news on Phys.org

Sep 29, 2007

fikus

you're right. Think where are the points with x^2+y^2+z^2=0.
You can write the domain as: [tex]\mathbb{R}^3 \setminus{\{0,0,0\}}[/tex]

Sep 29, 2007

HallsofIvy

Science Advisor

Homework Helper

Or:
[tex]\{ (x,y,z)| x^2+ y^2+ z^2\ne 0 \}[/tex]

1. What is a function with multiple variables?

A function with multiple variables is a mathematical relationship between two or more variables, where the value of one variable depends on the values of the other variables. It can be represented as f(x, y) or f(x, y, z), where x, y, and z are the variables.

2. How do you graph a function with multiple variables?

To graph a function with multiple variables, you will need to create a three-dimensional coordinate system, with one axis representing each variable. Then, plot points on the graph by substituting different values for the variables and connecting them to form a surface or curve.

3. What is the difference between a function with one variable and a function with multiple variables?

A function with one variable has only one input and one output, while a function with multiple variables has more than one input and one output. In other words, a function with multiple variables takes in multiple values and produces a single value as its output.

4. How do you find the domain and range of a function with multiple variables?

The domain of a function with multiple variables is the set of all possible values for the input variables, while the range is the set of all possible values for the output variable. To find the domain and range, you can use the graph of the function or solve for the variables algebraically.

5. Can you optimize a function with multiple variables?

Yes, functions with multiple variables can be optimized by finding the maximum or minimum values of the function. This can be done by taking partial derivatives and setting them equal to zero, then solving for the variables. This will give the coordinates of the maximum or minimum point on the graph of the function.