What are the domain and range of g of x equals the square root of the quantity x plus 4?

D: [4, ∞) and R: [0, ∞)
D: (–4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (4, ∞) and R: (–∞, 0)

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joaobezerra joaobezerra · Answer 1 · 2022-04-07T10:08:01+02:00

Using it's concept, it is found that the domain and range of the function are given by:

D: [–4, ∞) and R: [0, ∞)

The domain of a function is the set that contains all the values of the input.

The range of a function is the set that contains all the values of the output.

In this problem, the function is:

[tex]g(x) = \sqrt{x + 4}[/tex]

The square root function does not exist for negative values, hence the domain is represented by:

[tex]x + 4 \geq 0 \rightarrow x \geq -4[/tex]

The range of the square root function is [tex]x \geq 0[/tex], which remains the same as there are no vertical translations.

Hence the correct option is given by:

D: [–4, ∞) and R: [0, ∞)

More can be learned about domain and range of functions at https://brainly.com/question/10891721