Math Problem Statement

is it a function

Is the given relation a function?

Solution

Looking at the image, we see two sets with elements connected by arrows, which represent a relation between the two sets. To determine if this relation is a function, we need to check whether each element from the first set is connected to exactly one element in the second set. In other words, a function assigns one and only one output (element in the second set) to each input (element in the first set).

In this case, the elements of the first set are:

  • 1-1
  • 00
  • 11
  • 22

Each element of the first set is connected to exactly one element in the second set (no element in the first set is connected to multiple elements).

Thus, this relation is a function.

Would you like further details or have any additional questions?

Here are five related questions you might consider:

  1. How do you determine if a relation is a one-to-one function?
  2. Can a function have elements in the second set that are not used?
  3. What is the difference between a function and a relation?
  4. What are the characteristics of a bijection?
  5. How can you represent this function as a set of ordered pairs?

Tip: In a function, no input (element in the domain) should have more than one output, but multiple inputs can have the same output.

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Math Problem Analysis

Mathematical Concepts

Functions
Relations
Set Theory

Formulas

-

Theorems

Definition of a Function

Suitable Grade Level

Grades 8-10