Question

Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function.

Answer 1

Answer:

The parent function is $y=\sqrt[3]{x}$.

The function is translated 4 units to the left followed by horizontal compress by a factor of $\frac{1}{2}$ and then reflection across y-axis.

Step-by-step explanation:

We are given,

The transformed function is $y=\sqrt[3]{-8x-4}$.

Now, we see that,

The function is translated 4 units to the left, which gives us the translated function $y=\sqrt[3]{-8x}$.

The function is first compressed horizontally by a factor of $\frac{1}{2}$, which gives $y=\sqrt[3]{-x}$.

Now, this function is reflected across y-axis, which gives the parent function $y=\sqrt[3]{x}$.

Hence, we see that,

The parent function is $y=\sqrt[3]{x}$.

The function is translated 4 units to the left followed by horizontal compress by a factor of $\frac{1}{2}$ and then reflection across y-axis.

Answer 2

The correct answer is:

Compared to the parent graph, this graph is compressed horizontally, reflected across the y-axis, and shifted right 4 units.

Explanation:

The parent function in this situation is $y=\sqrt[3]{x}$.

Algebraically, the changes we can see from the parent function to this function is that the variable is multiplied by 8, negated, and had 4 subtracted from it.

When we negate the variable, this reflects the graph across the y-axis.

When we multiply the variable by a number greater than 1, this horizontally compresses the graph.

When we subtract a number from the variable before taking the cubed root, this shifts the graph horizontally; specifically, it shifts it to the right.

Thus the graph will be reflected across the y-axis, horizontally compressed by 1/8, and shifted 4 units to the right.