Domain Range 816C48

1. **State the problem:** We need to determine the correct statement about the domain and range of the function $$f(x) = \sqrt{-x}$$. 2. **Recall the domain rule for square root functions:** The expression inside the square root must be greater than or equal to zero for the function to be real-valued. 3. **Find the domain:** $$-x \geq 0 \implies x \leq 0$$ So, the domain is all real numbers less than or equal to zero. 4. **Find the range:** Since the square root function outputs values greater than or equal to zero, and here we have $$f(x) = \sqrt{-x}$$, the output values are $$f(x) \geq 0$$. 5. **Check the statements:** - "The domain of the function is all real numbers greater than or equal to 0." This is false because domain is $$x \leq 0$$. - "The range of the function is all real numbers greater than or equal to -1." This is false because the range starts at 0, not -1. - "The range of the function is all real numbers less than or equal to 0." This is false because the range is $$f(x) \geq 0$$. - "The domain of the function is all real numbers less than or equal to 0." This is true. **Final answer:** The correct statement is: "The domain of the function is all real numbers less than or equal to 0."