Answer:
[tex](x,y)\rightarrow (4x+12,-4y+16)[/tex]
Step-by-step explanation:
1 transformation - translation 3 units to the right and 4 units down. This translation has the rule
[tex](x,y)\rightarrow (x+3,y-4)[/tex]
2 transformation - reflection across the x-axis. This reflection has the rule
[tex](x,y)\rightarrow (x,-y)[/tex]
3 transformation - dilation by a factor of 4 with the origin as the center of dilation. This dilation has the rule
[tex](x,y)\rightarrow (4x,4y)[/tex]
Now, the sequence of these three transformation has the rule
[tex](x,y)\rightarrow\limits^{\text{1st transformation}} (x+3,y-4)\rightarrow\limits^{\text{2nd transformation}}(x+3,-(y-4))\rightarrow\limits^{\text{3rd transformation}} (4(x+3),4(-(y-4)))\\ \\(x,y)\rightarrow (4x+12,-4y+16)[/tex]
