The range of which function includes –4? \begin{aligned} & \Theta \quad y = \sqrt{x} - 5 \\ & \Theta \quad y = \sqrt{x} + 5 \\ & \Theta \quad y = \sqrt{x + 5} \\ & \Theta \quad y = \sqrt{x - 5} \end{aligned}
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Understand the range of square root functions

- The range of $$\sqrt{x}$$ is $$[0, \infty)$$, meaning all non-negative real numbers
- This constraint will help us determine which function can produce - 4

Step 3:
: Analyze each function's range

- Range is $$[0, \infty)
- This function CAN produce - 4 - This function CANNOT produce - 4 - This function CANNOT produce - 4 - This function CANNOT produce - 4

Final Answer

Option 1, y = \sqrt{x} - 5, is the function whose range includes - 4.