Final answer:
To determine the transformations used to create the image on a graph, one must understand reflections, translations, and rotations within the coordinate system. These transformations manipulate the position and orientation of the object in relation to axes and directions such as horizontally to the right and vertically upward.
Step-by-step explanation:
In order to describe the transformations that were used to create the image on the graph, it is essential to understand certain key concepts and directions within the coordinate system. A reflection over the x-axis will change the sign of the y coordinate of each point, causing the image to appear inverted vertically. A translation is the sliding of an object without rotation; a translation 6 units right means the object is moved horizontally to the right side without any change in its orientation. A reflection over the y-axis would similarly change the sign of the x coordinate of each point, but the image would flip horizontally. Finally, a rotation is a circular motion around an axis; a rotation 90 degrees clockwise means that the object is turned to its right side by 90 degrees, while a rotation 90 degrees counterclockwise is a turn to its left.
A reflection over the x-axis and a translation 6 units to the right would involve flipping the object upside down (vertically) and then moving it c. horizontally to the right side of the coordinate system. A rotation 90 degrees clockwise and a reflection over the x-axis would mean the object turns 90 degrees from its original position in a d. clockwise direction and then flips vertically. A translation 10 units to the right and reflection over the x-axis would mean the object moves 10 units to the right (c. horizontally to the right side of the coordinate system) before flipping vertically. Lastly, a reflection over the y-axis and rotation 90 degrees counterclockwise would flip the object horizontally before rotating it to the left side.