Original Function:
[tex]\sf\sqrt[\sf 3]{\sf x}[/tex]
If you add something inside the square root, it will shift the graph of the function to the left that same amount of units.
Example: [tex]\sf\sqrt[\sf 3]{\sf x+4}[/tex]
Shifts the original function to the left 4 units.
If you subtract something inside the square root, it will shift the graph of the function to the right that same amount of units.
Example: [tex]\sf\sqrt[\sf 3]{\sf x-6}[/tex]
Shifts the original function to the right 6 units.
If you add something outside of the square root, it will shift the graph of the function up that same amount of units.
Example: [tex]\sf\sqrt[\sf 3]{\sf x}+3[/tex]
Shifts the original function up 3 units.
If you subtract something outside of the square root, it will shift the graph of the function down that same amount of units.
Example: [tex]\sf\sqrt[\sf 3]{\sf x}-2[/tex]
Shifts the original function down 2 units.
So in the case of [tex]\sf\sqrt[\sf 3]{\sf x+6}-8[/tex], it will shift the original function 6 units to the left and 8 units down.
The domain is the x-values. The x-values of the original function is all real numbers. Shifting the graph down and to the left would not change the domain.
The range is the y-values. The y-values of the original function is all real numbers. Shifting the graph down and to the left would not change the domain.
So your answer is C.
