The parent function is y = f(x)
The derived function is y = -f(x - 4) + 3
The sequence of transformations that was done to the graph of y = f(x) is:
• The function y = f(x) is shifted to the right by 4 units to become y = f(x - 4)
,
• The function y = f(x-4) is dilated by a factor of -1 to become y = -f(x - 4). This also means a 180 degrees rotation
,
• The function y = -f(x - 4) is shifted up by 3 units to become y = -f(x - 4) + 3
In summary, the transformations done to graph of y = f(x) in the order that they occur are:
0. Translation to the right by 4 units
,
1. Dilation by a factor of -1
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2. Translation upwards by 3 units