Answer:
[tex]\sqrt[3]{x} -3[/tex]: The parent graph will move 3 units down.
[tex]\sqrt[3]{x-3}[/tex]: The parent graph will move 3 units right.
Step-by-step explanation:
The parent function [tex]\sqrt[3]{x}[/tex] 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 [tex]\sqrt[3]{x} -3[/tex] 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 [tex]\sqrt[3]{x-3}[/tex] 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:
- parent function graph
- parent function graph moved 3 units down
- parent function graph moved 3 units right
- parent function graph and the two transformations
