# General function in 2 variables

• Emilijo
In summary, the task is to find a general function in 2 variables that is periodic and includes blue and red points in each example. The value of the function must be 1 in blue points and 0 in red points. The appearance of the function is not important as long as it meets these terms. The poster has attempted to use sine, absolute value, and Fourier series, but is struggling to find a solution. They are asking for help and clarification on how to approach this problem.
Emilijo

## Homework Statement

I need to get a general function in 2 variables f(m,n).
The task is to find a general function f(m,n) with these terms:
The function has to be periodic.
The function has to include those blue and red points in each example.
The value of the function has to be f(m,n) =1 ONLY in blue points, and the value of the function has to be f(m,n)=0 ONLY in red points.

The look of the function isn't important as long as it complies with previous terms.

## Homework Equations

You can see a graphicon with charasteristic points:
In the first example m=2 (m is period).

In the next example m=3:

For m=4:

and so on.

## The Attempt at a Solution

In first example (for m=2) I used functions: sin and absolute, but for all other m,
it is not possible with only those functions, I also tried use the Fourier series but I don't have so
much knowledge in mathematics to built a such function.
Does somebody know how to do it?

#### Attachments

• m2.png
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• m3.png
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• m4.png
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Last edited:
Emilijo said:

## Homework Statement

I need to get a general function in 2 variables f(m,n).
The task is to find a general function f(m,n) with these terms:
The function has to be periodic.
The function has to include those blue and red points in each example.
The value of the function has to be f(m,n) =1 ONLY in blue points, and the value of the function has to be f(m,n)=0 ONLY in red points.

The look of the function isn't important as long as it complies with previous terms.

## Homework Equations

You can see a graphicon with charasteristic points:
In the first example m=2 (m is period).

In the next example m=3:

For m=4:

and so on.

## The Attempt at a Solution

What have you done so far? You must show some work and exhibit some effort before receiving help in this Forum.

RGV

Ray Vickson said:
What have you done so far? You must show some work and exhibit some effort before receiving help in this Forum.

RGV

I tried and wrote about it above in previous post.

Emilijo said:
I tried and wrote about it above in previous post.

Your previous post did not show any work; it just said you had tried some things, but did not show exactly what you did.

RGV

## What is the general function in 2 variables?

The general function in 2 variables is a mathematical expression that relates two variables, typically denoted as x and y, to each other. It can take on various forms, such as linear, quadratic, exponential, or trigonometric functions. It allows us to study the relationship between two variables and make predictions or analyze patterns.

## What is the difference between a function and a general function in 2 variables?

A function is a mathematical rule that assigns a unique output value to every input value. It is typically written as f(x) and has a single independent variable. On the other hand, a general function in 2 variables has two independent variables, x and y, and can take on different forms. The output value is dependent on both variables, and the relationship between them can vary.

## How do you graph a general function in 2 variables?

To graph a general function in 2 variables, we can plot points on a coordinate plane. Each point represents a pair of input values (x and y) and their corresponding output value. We can also use level curves or contour lines to represent the function graphically. These curves connect points with the same output value, creating a visual representation of the function's behavior.

## What is the importance of studying general functions in 2 variables?

Studying general functions in 2 variables allows us to understand the relationship between two variables and how they affect each other. This is crucial in many fields, such as physics, economics, and engineering, where multiple variables interact with each other. It also helps us make predictions and analyze patterns, which can have practical applications in real-world problems.

## What are some real-life examples of general functions in 2 variables?

General functions in 2 variables can be found in many real-life situations. For example, the relationship between the price of a product and the demand for it can be represented by a general function. The amount of rainfall in a specific area can also be described by a general function in terms of time and location. In physics, the trajectory of a projectile can be modeled using a general function in 2 variables, where the variables are time and distance.

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