Answer:
The only statement which is correct:
''The range of the graph is all real numbers less than or equal to 0''.
Hence, option a) is correct.
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\sqrt{-x}[/tex]
Determining the domain:
The domain of a function is the set of input or argument values for which the function is real and defined
It is clear that the value or radicand inside the radical must be greater than or equal to zero, otherwise, the function will be undefined.
i.e.
[tex]-x\ge 0[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex]\left(-x\right)\left(-1\right)\le \:0\cdot \left(-1\right)[/tex]
Simplify
[tex]x\le \:0[/tex]
Thus, the domain of a function is:
[tex]x\le \:0[/tex]
In other words, the domain of the graph is all real numbers less than or equal to 0.
Determining the range:
The set of values of the dependent variable for which the function is defined
The range of a radical function of the form
[tex]c\sqrt{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k[/tex]
[tex]k = 0[/tex]
[tex]f\left(x\right)\ge \:0[/tex]
Therefore, the only statement which is correct:
''The range of the graph is all real numbers less than or equal to 0''.
Hence, option a) is correct.
