Domain is the set of x values that makes the function have a defined value.
The given function :
[tex]g(x)=\sqrt[3]{x-5}[/tex]
Note that you can take a cube root of both positive and negative numbers, so all real values of x can be a value of x in the radicand.
Domain : (-∞, ∞)
Filling up the table, substitute the values of x to the function.
[tex]\begin{gathered} g(5)=\sqrt[3]{5-5}=0 \\ g(6)=\sqrt[3]{6-5}=1 \\ g(-3)=\sqrt[3]{-3-5}=-2 \\ g(13)=\sqrt[3]{13-5}=2 \\ g(4)=\sqrt[3]{4-5}=-1 \end{gathered}[/tex]
The graph will be :
The answer is Choice B.
