Which sequence of transformations will result in an image that maps onto
itself?

The correct answer is:

D) reflect over the y axis and then reflect again over the y axis.

Explanation:

Logically, if we reflect a figure across the y-axis and then reflect across the y-axis again, we have undone what we originally did, and the figure is back in its original position.

Algebraically, reflecting across the y-axis maps every point (x, y) to (-x, y). Reflecting this point across the y-axis maps (-x, y) to (x, y); this is our original point.