What set of reflections would carry rectangle abcd onto itself? rectangle abcd is shown. a is at 1, 1 and b is at 1, 3 and c is at 4, 3 and d is at 4, 1. y-axis, x-axis, y-axis x-axis, y-axis, y-axis x-axis, y=x, x-axis, y=x y=x, x-axis, y=x, y-axis

  y=x, x-axis, y=x, y-axis

Explanation:

Reflecting the figure across three axes just moves it from one quadrant to another. It does not map the figure to itself.

Reflecting across the line y=x moves it from quadrant II to IV or vice-versa. If it is in quadrant I or III, it stays there. So the sequence of reflections x-axis (moves from I to IV), y=x (moves from IV to II), x-axis (moves from II to III), y=x (stays in III) will not map the figure to itself.

However, the last selection will map the figure to itself. The initial (and final) figure location, and the intermediate reflections are shown in the attached. The figure starts and ends as blue, is reflected across y=x to green, across x-axis to orange, across y=x to red, and finally across y-axis to blue again.

step-by-step explanation:

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.