Question

which of the following the range of function includes -4? A. y=sqrt(x)-5 B. y=sqrt(x)+5 C. y=sqrt(x+5) D. y=sqrt(x-5)

Answer 1

All of the equations contain -4 in their range.
A) -4 = sqrt(x) - 5
1 = sqrt(x)
x = 1; valid
B) -4 = sqrt(x) + 5
-9 = sqrt(x)
x = 81; valid
C) -4 = sqrt(x + 5)
16 = x + 5
x = 11; valid
D) -4 = sqrt(x - 5)
16 = x - 5
x = 21
I believe the equations contain square instead of square root, in which case the answer would be A because no other could have a negative range.

Answer 2

For option A: y = sqrt(x) - 5. Range is {f(x) | f(x) ≥ -5}

For option B: y = sqrt(x) + 5. Range is {f(x) | f(x) ≥ 5}

For option C: y = sqrt(x + 5). Range is {f(x) | f(x) ≥ 0}

For option D: y = sqrt(x - 5). Range is {f(x) | f(x) ≥ 0}