which relation(s) best shows y as a function of x?

Question

A: input -2, output 0. input 1, output 8. Input 4, output 5. input 7, output 11.

B: input -2, output 3 and 4. input 6, output 2. input 10, output 5.

C: input 1, 4, 7, output 5.

D: input, 8, output -5, 1, 3, 6

Answer 1

To determine which relation(s) best show \( y \) as a function of \( x \), we need to check if each input \( x \) is associated with one and only one output \( y \).

• A:

  • Input: -2 → Output: 0
  • Input: 1 → Output: 8
  • Input: 4 → Output: 5
  • Input: 7 → Output: 11
  • Conclusion: Each input corresponds to a unique output. This is a function.

• B:

  • Input: -2 → Output: 3 and 4 (two outputs for one input)
  • Input: 6 → Output: 2
  • Input: 10 → Output: 5
  • Conclusion: The input -2 has two outputs (3 and 4). This is not a function.

• C:

  • Input: 1 → Output: 5
  • Input: 4 → Output: 5
  • Input: 7 → Output: 5
  • Conclusion: Each input corresponds to a unique output (5), even though multiple inputs give the same output. This is a function.

• D:

  • Input: 8 → Output: -5
  • Input: 1 → Output: 3
  • Input: 6 → Output: ? (not specified in the relation)
  • Conclusion: Without more information, we can't confirm if all inputs have one unique output. However, with the given data, we assume each is unique as stated. This can be a function, but it's not clear based on the given data.

Thus, the relations that show \( y \) as a function of \( x \) are:

• A
• C

So, the best answer is: A and C.