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If f(x) = |x| and g(x) = |x| − 4, which translation is applied to f(x) to get g(x)? A. a vertical translation of f(x) four units upward B. a horizontal translation of f(x) four units to the left C. a horizontal translation of f(x) four units to the right D. a vertical translation of f(x) four units downward

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Answer:

D. A vertical translation of f(x) four units downward.

Step-by-step explanation:

Recall that the transformations form of an absolute value function is:

f(x) = ±a|b(x-h)|+k

Where 'a' is a vertical stretch/compression

'b' is a horizontal stretch/compression

'h' is a horizontal shift

'k' is a vertical shift

In g(x) = |x| -4, we can derive a k value of -4.

This means that from f(x) to g(x), there has been a vertical translation of f(x) four units downward.

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