Answer:
Z.
Step-by-step explanation:
Since we are dealing with a cubic root function, we can obtain the graph of our function transforming the parent cube root function [tex]g(x)=\sqrt[3]{x}[/tex].
Subtracting 1 to the input will shift the graph of the parent cube root function 1 units to the right, so the minus 1 in [tex]g(x)=\sqrt[3]{x-1}[/tex] will shift the graph 1 units right.
Now, remember that the cubic root function is and odd function, which means it is symmetric about the origin. So, multiplying the [tex]x[/tex] inside the cube root will reflect the graph about the origin [tex]g(x)=\sqrt[3]{-x-1}[/tex].
Therefore, the graph our function [tex]f(x)=\sqrt[3]{-x-1}[/tex] is the graph of the parent function [tex]g(x)=\sqrt[3]{x}[/tex] shifted 1 unit to the right and then reflected about the origin.
We can conclude that the correct answer is Z.
