Using translation concepts, the method that Howard could have used to determine the coordinates of the vertices of the image is:
(x,y) -> (-x,y).
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A reflection over the y-axis can be described according to the following rule:
(x,y) -> (-x,y).
Hence this rule can be applied to find the vertices.
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