the function f(x)= -\\sqrt{-x} is shown on the graph. which statement is correct? the range of the graph is…

Answer:

The range of the graph is all real numbers greater than or equal to 0.

Explanation:

Step1: Determine the domain

For the function $f(x)=-\sqrt{-x}$, the expression under the square - root must be non - negative. So, $-x\geq0$, which gives $x\leq0$. The domain is all real numbers $x$ such that $x\leq0$.

Step2: Determine the range

The square - root function $\sqrt{-x}\geq0$. Then $-\sqrt{-x}\leq0$. So the range of the function $y = f(x)$ is all real numbers $y$ such that $y\leq0$. The first statement "The range of the graph is all real numbers greater than or equal to 0" is incorrect. The second statement "The domain of the graph is all real numbers greater than or equal to 0" is incorrect as the domain is $x\leq0$. The third statement "The range and domain of the graph are the same" is incorrect. The fourth statement "The domain of the graph is all real numbers" is incorrect. There seems to be an error in the provided options as the correct range is all real numbers less than or equal to 0. But if we assume a mis - typing in the first option and it was meant to be "The range of the graph is all real numbers less than or equal to 0", then that would be the correct answer.