Question

Please help me with this parent function

Answer 1

`\sqrt[3]{x} -3`: The parent graph will move 3 units down.

`\sqrt[3]{x-3}`: The parent graph will move 3 units right.

Explanation:

The parent function
`\sqrt[3]{x}` looks like the first image attached.

Using knowledge of transformations, numbers outside the radical move the graph up or down (vertically). A positive number moves the graph up; a negative number moves the graph down.

Numbers inside the radical move the graph left or right (horizontally). A positive number moves the graph left; a negative number moves the graph right.

In the first transformation
`\sqrt[3]{x} -3` the number is outside of the radical, meaning that the graph will move vertically. The 3 is negative, so the graph will move 3 units down.

The first transformation moves the parent graph 3 units down.

In the second transformation
`\sqrt[3]{x-3}` the number is inside the radical so the graph will move horizontally. The 3 is negative so the graph will move 3 units to the right.

The second transformation moves the parent graph 3 units right.

The attached images show:

1. parent function graph
2. parent function graph moved 3 units down
3. parent function graph moved 3 units right
4. parent function graph and the two transformations