Question

What is the domain and range of the given function? Is it a function?

1) (0, infinity), [4, 4], Yes
2) (0, infinity), (4, 4), No
3) (0, infinity), [4, 4], No
4) (0, infinity), (4, 4), Yes

Answer 1

The correct domain and range presented in the options is (0, infinity) and [4, 4], respectively, and it describes a function, meaning the correct answer is Option 1.

Step-by-step explanation:

The domain and range of a function describe which values the function's inputs (x-values) and outputs (y-values) can take, respectively. A function is defined as a relation where each input has a uniquely associated output. In the given options, the domain of the function is described as (0, infinity), meaning the function is defined for all positive real numbers. The range is where the answers differ.

Option 1 suggests the range is [4, 4], indicating that the function outputs the single value 4 for all inputs in the domain. This would indeed describe a function, specifically a constant function. Option 3 is identical except it denies that this describes a function, which is incorrect under standard definitions of a function.