Question

Which of the following graphs corresponds to the function above? ^3√(-x-1)

Answer 1

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 $g(x)=\sqrt[3]{x}$.

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 $g(x)=\sqrt[3]{x-1}$ 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 $x$ inside the cube root will reflect the graph about the origin $g(x)=\sqrt[3]{-x-1}$.

Therefore, the graph our function $f(x)=\sqrt[3]{-x-1}$ is the graph of the parent function $g(x)=\sqrt[3]{x}$ shifted 1 unit to the right and then reflected about the origin.

We can conclude that the correct answer is Z.