Question

The function f(x)=-√-x is shown on the graph. Which statement is correct? The range of the graph is all real numbers greater than or equal to 0. The domain of the graph is all real numbers greater than or equal to 0. The range and domain of the graph are the same. The domain of the graph is all real numbers.

Answer 1

The correct option is:    The range and domain of the graph are the same.

Explanation

Given function is:   $f(x) = -\sqrt{-x}$

The inside term of a square root can't be negative, it will be always 0 or positive. That means,  $-x \geq 0$ or $x\leq 0$

So, the Domain of the function is : "All real numbers such that $x\leq 0$"

Now, if x=0, then f(x) =0 and if x is any negative number, then f(x) will be also negative.

That means, the Range of the function: "All real numbers such that $f(x)\leq 0$"

So, the range and domain of the function are the same.