Which function has the same range as y = - 2 sqrt of x-3+8?

Given:

-2 √ (x - 3) + 8

Solution:

Square root is always non-negative, so minimum value is 0.

So, this function has range (-∞, 8]

√ (x - 3) - 8 has range [-8, ∞)

√ (x - 3) + 8 has range [8, ∞)

-√ (x + 3) + 8 has range [-∞, 8)

-√ (x - 3) - 8 has range [-∞, - 8)

Therefore, the equation g (x) = - sqrt x + 3 + 8 is the only one with the same range as - 2 √ (x - 3) + 8.

You usually tell what kind of numbers the domain (x) and range (f (x)) values are allowed when defining a function.