Answer:
The domain of the graph is all real numbers less than or equal to 0
Step-by-step explanation:
we have the function
[tex]f(x)=\sqrt{-x}[/tex]
we know that
The radicand must be positive
so
[tex]-x \geq 0[/tex]
Solve for x
Multiply by -1 both sides
[tex]x\leq 0[/tex]
The domain is the interval ------> (-∞,0]
All real numbers less than or equal to zero
The range of the function is the interval -----> [0,∞)
[tex]f(x)\geq 0[/tex]
see the attached figure to better understand the problem
All real numbers greater than or equal to zero
Verify each statement
case 1) The domain of the graph is all real numbers
The statement is false
Because, the domain is all real numbers less than or equal to zero
case 2) The range of the graph is all real numbers
The statement is false
Because, the range is all real numbers greater than or equal to zero
case 3) The domain of the graph is all real numbers less than or equal to 0
The statement is true
case 4) The range of the graph is all real numbers less than or equal to 0
The statement is false
Because, the range is all real numbers greater than or equal to zero
