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Question: Which of the following represents the equation of the graph obtained by a vertical translation of 7 units downwards followed by a reflection across the y-axis on the graph of y = f(x)?


A ) y = 7 - f(x)
B ) y = - f(x - 7)
C ) y = f(- x) - 7
D ) y = f(x) - 7

Steps to derive

1 y = f(x) - 7 represents the equation of the graph obtained by a vertical translation of 7 units down on the graph of y = f(x).

2 The reflection of y = f(x) - 7 across the y-axis is y = (f(- x) - 7) = f(- x) - 7.

3 So, y = f(- x) - 7 represents the equation of the graph obtained by a vertical translation of 7 units down followed by a reflection across the y-axis on the graph of y = f(x).



Hence the right answer is Option C

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