Math Problem Statement

Determine whether the relation is a​ function, and give the domain and range. 24 8 4 13 15

Solution

To determine whether a relation is a function, we need to know if each input (domain) is associated with exactly one output (range). In the given problem, it appears that only values are provided without a clear relation between them. Therefore, we need to clarify the nature of the relation.

Assuming these numbers represent outputs associated with some inputs, we can't definitively determine if it's a function without knowing the inputs. Let's assume the given numbers are part of an ordered pair relation, such as:

{(x1,24),(x2,8),(x3,4),(x4,13),(x5,15)}\{ (x_1, 24), (x_2, 8), (x_3, 4), (x_4, 13), (x_5, 15) \}

We need to verify that each input xx maps to exactly one output yy.

Domain and Range:

  1. Domain: The set of all possible inputs xx. Without specific inputs given, we can only say that the domain is {x1,x2,x3,x4,x5}\{ x_1, x_2, x_3, x_4, x_5 \}.
  2. Range: The set of all possible outputs yy. Given the numbers provided:
    • Range: {24,8,4,13,15}\{ 24, 8, 4, 13, 15 \}

Checking if it's a Function:

  • Since each xx must map to exactly one yy, if we assume no repeated xx values, this relation is a function. If any input xx maps to more than one yy, it is not a function.

However, based on the given numbers, there is no indication of repeated values or multiple mappings. Therefore, assuming unique inputs, the relation can be considered a function.

Summary:

  • Relation: Function (assuming unique inputs)
  • Domain: {x1,x2,x3,x4,x5}\{ x_1, x_2, x_3, x_4, x_5 \}
  • Range: {24,8,4,13,15}\{ 24, 8, 4, 13, 15 \}

Would you like to provide additional information or clarify the inputs? If you have any questions or need more details, please let me know.

Relative Questions:

  1. What is a mathematical function, and how is it defined?
  2. How do you determine the domain of a function?
  3. How do you determine the range of a function?
  4. What is the difference between a function and a relation?
  5. Can a function have the same output for different inputs?
  6. How can we visually represent a function using a graph?
  7. What are some examples of common mathematical functions?
  8. How does the vertical line test help determine if a graph represents a function?

Tip:

When analyzing functions, always ensure that each input value maps to exactly one output value to meet the definition of a function.