Question about the definition of functions

You are trying to understand the meaning of the notation used to define a set. The ":" is used to mean "such that" and the "x e X" means that x is an element of the set X. In summary, the set Y is defined as the set of all y values such that y equals f(x) for x an element of the set X. Additionally, the function f's graphic is a region of points in the xy plane, defined as the set of all points (x,y) such that y=f(x) and x is an element of the set X. The ":" symbol is used to indicate "such that" in this notation.
  • #1
vaazu
21
0

Homework Statement


Y={y:y=f(x), xe(can´t find the right symbol, but it should be belongs)X} is the changing region (is it like that in English?) of the function f

function f-s graphic is a region of points in the xy plane is defined as (f)={(x;y):y=f(x),x e X0

Homework Equations


what do the :y mean? I doubt that means divided by y that's why I want to know what does it mean?


The Attempt at a Solution

 
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  • #2
Your definition in english reads, Y is equal to the set of all y such that y=f(x) for x an element of X. The ':' is the 'such that'.
 
  • #3
vaazu said:

Homework Statement


Y={y:y=f(x), xe(can´t find the right symbol, but it should be belongs)X} is the changing region (is it like that in English?) of the function f
Your set is the set of all possible y values. The English term is "range" of f. In "higher mathematics" that might be called the "image" of whatever the domain (values of x) is.

function f-s graphic is a region of points in the xy plane is defined as (f)={(x;y):y=f(x),x e X0

Homework Equations


what do the :y mean? I doubt that means divided by y that's why I want to know what does it mean?
You used it in your first set! It mean "such that". Often a vertical line "|" is used to mean the same thing.

The Attempt at a Solution

 

1. What is a function?

A function is a mathematical concept that relates an input (or inputs) to an output. It takes in a value or values and performs a specific operation on them, resulting in a single output.

2. What is the purpose of using functions?

Functions are used to organize and modularize code, making it more efficient and easier to read and maintain. They also allow for the reuse of code, as they can be called multiple times with different inputs.

3. How do you define a function?

A function is typically defined by using the keyword "function", followed by the function name, a set of parentheses that may contain parameters, and a set of curly braces that contain the code to be executed when the function is called.

4. What are parameters in a function?

Parameters are the values that are passed into a function when it is called. They act as placeholders for the actual values that will be used in the function's calculation or operation.

5. How does a function differ from a method?

A function is a standalone piece of code that performs a specific operation, while a method is a function that is associated with an object or class. Methods are typically used in object-oriented programming, while functions can be used in any programming language.

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