Domain is the set of x values that makes the function have a defined value.
The given function :
![g(x)=\sqrt[3]{x-5}](https://img.qammunity.org/2023/formulas/mathematics/college/agbx0d9f4yift8izwxia3jsdy7xsra04g3.png)
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.
![\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}](https://img.qammunity.org/2023/formulas/mathematics/college/mccv3bjlxtmbt733zxe3f8pcoy70e41eos.png)
The graph will be :
The answer is Choice B.