Question

Which function has the same range as . . . see attached

Answer 1

Answer:

$g(x)=-\sqrt{x+3}+8$

Step-by-step explanation:

we have

$f(x)=-2\sqrt{x-3}+8$

using a graphing tool

see the attached figure N $1$

The domain is the interval ------> [3, ∞)

The range is the interval ------> (-∞, 8]

Verify the range of each case by graphing tool

see the attached figure N $2$

case A) $g(x)=\sqrt{x-3}-8$

The range is the interval ------> [-8,∞)

case B) $g(x)=\sqrt{x-3}+8$

The range is the interval ------> [8,∞)

case C) $g(x)=-\sqrt{x+3}+8$

The range is the interval ------>(-∞, 8] ----> is the solution (same range that f(x))

case D) $g(x)=-\sqrt{x-3}-8$

The range is the interval ------> (-∞, -8]

Answer 2

First lets find the range of -2 sqrt(x - 3) + 8
x cannot be < 3   or f(x) would not be real  

when x = 3 f(x) = 8 
and for all other values of x  f(x) will tend to  - infinity

range is [8, - infinity)

if we do same for the 4 choices we'll see that  - sqrt(x - 3)+8  will have same range