Question

if a figure needs to be reflected across the x - axis and is translated down 3, then these two mappings can be combined as option #1: (x,y)→(x, - y - 3). option #2: (x,y)→(x,y - 3). option #3: (x,y)→( - x - 3,y). option #4: (x,y)→(x - 3,y). (1 point)

Explanation:

Step1: Reflection across x - axis

When a point $(x,y)$ is reflected across the $x$-axis, the $x$-coordinate remains the same and the $y$-coordinate changes its sign. So, $(x,y)\to(x, - y)$.

Step2: Translation down 3 units

After reflection, when we translate the point down 3 units, we subtract 3 from the $y$-coordinate. So, $(x,-y)\to(x,-y - 3)$.

Answer:

Option #1: $(x,y)\to(x,-y - 3)$