Question

Determine whether each relation is a function. If it is, state its domain and range.

A) Not a function

B) Function; Domain: -2, 0, 3, 8; Range: 1, -1, 2, 4, -5

C) Function; Domain: -2, 0, 3, 8; Range: 1, -1, 2, 4, -5

D) Not a function

Answer 1

To determine if a relation is a function, each input should have exactly one output. Option B and C are functions with defined domains and ranges, while A and D are not functions.

Step-by-step explanation:

To determine whether each relation is a function, we need to check if for every input there is exactly one output. A relation is a function if each input leads to only one output. This aligns with the definition of a function in mathematics. Therefore:

• Option A: Not a function. This could be due to the relation having a discontinuity or being double-valued.
• Option B: Function; here we have a well-defined list of inputs and outputs, so it's a function. The domain is the set {-2, 0, 3, 8}, and the range is the set {1, -1, 2, 4, -5}.
• Option C: Also a function; it has the same domain and range as Option B.
• Option D: Not a function. Without specific details, it is hard to tell why this option is not a function. It could imply a multiple output situation for a single input.

It's important to remember that functions must have only one output for every input within their domain to be defined as a function.