High School

Create your own functions given the following conditions:

- Domain: Positive even integers
- Codomain: Positive odd integers

Identify which category each function belongs to:

A. Function
B. Not a function
C. One-to-one
D. Onto
E. Both one-to-one and onto
F. One-to-one but not onto

Answer :

Final answer:

The provided examples show different types of functions with a domain of positive even integers and a codomain of positive odd integers. These include simply' a function', 'not a function', 'one-to-one', 'onto', 'both one-to-one and onto', 'one-to-one but not onto'.

Explanation:

The question pertains to different types of functions with a domain of positive even integers and a codomain of positive odd integers. Here are examples for each type requested:

  1. Function: Example function could be f(x)=2x+1, which matches any given even integer to a positive odd integer.
  2. Not a Function: We can not create a setup where the specific conditions given do not form a function because each input (domain) is sent to a unique output (codomain).
  3. 1 to 1: Example function could be g(x)=2x+1. Each element in the domain maps to exactly one unique element in the codomain.
  4. Onto: Example function could be h(x)=2x+1. Every possible output in the codomain is paired with at least one input from the domain.
  5. Both 1 to 1 and Onto: Example function could be f(x) = 2x + 1. In this case, the function is both one-to-one and onto since every input from the domain is mapped to a unique output in the codomain and all elements in the codomain are used.
  6. 1 to 1 but not Onto: Example function could be f(x) = 2x + 3. In this case, the function is one-to-one but not onto. This means that every input from the domain is mapped to a unique output in the codomain, but not all elements in the codomain are used.

Learn more about Functions here:

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