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If the function y=-f(x-4)+3 were graphed, write the transformations to the graph of y = f(x) in theorder that they occur.

User Ragnar
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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)

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• 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

User Grigoryants Artem
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