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

Explanation:

Step1: Recall domain - definition

For the function $y = \sqrt{-x}$, the expression under the square - root must be non - negative. So, $-x\geq0$, which gives $x\leq0$. The domain is the set of all possible $x$ values.

Step2: Recall range - definition

The square - root function $\sqrt{-x}$ always gives a non - negative output. That is, $y=\sqrt{-x}\geq0$. The range is the set of all possible $y$ values.

Step3: Analyze each option

• Option 1: The range is $y\geq0$, not $y\leq0$.
• Option 2: Since $-x\geq0$ implies $x\leq0$, the domain is all real numbers less than or equal to 0. This is correct.
• Option 3: Domain is $x\leq0$ and range is $y\geq0$, they are not the same.
• Option 4: The range is $y\geq0$, not all real numbers.

Answer:

The domain of the graph is all real numbers less than or equal to 0.