Problem

Transformation Rule: $(x, y) \rightarrow$
\begin{tabular}{|l|l|}
\hline $\begin{array}{c}\text { Preimage Coordinates } \\
(x, y)\end{array}$ & \multicolumn{1}{c|}{ Image } \\
\hline$(2,-1)$ & $(-2,0)$ \\
\hline$(2,-3)$ & $(-2,-2)$ \\
\hline$(4,-3)$ & $(0,-2$ \\
\hline
\end{tabular}

Answer

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Answer

Final Answer: The transformation rule is \(\boxed{(x, y) \rightarrow (-x, y+1)}\).

Steps

Step 1 :Observe the given preimage and image coordinates.

Step 2 :Identify the transformation rule by comparing the preimage and image coordinates.

Step 3 :The transformation rule seems to be a combination of translation and reflection. The x-coordinate is reflected over the y-axis (multiplied by -1) and the y-coordinate is translated up by 1 unit.

Step 4 :Test the transformation function with the given preimage coordinates to see if it produces the correct image coordinates.

Step 5 :The transformation function is producing the correct image coordinates for the given preimage coordinates.

Step 6 :Therefore, the transformation rule is correct.

Step 7 :Final Answer: The transformation rule is \(\boxed{(x, y) \rightarrow (-x, y+1)}\).

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