Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

Correct answer marked below

The graph will move up by 2 units

The graph will move down by 2 units

The graph will move right by 2 units

Correct

The graph will move left by 2 units

Cannot be determined

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Explanation

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Official Explanation

Official

First, simplify f(x):

f(x) = (x + 2)^2 - (x - 2)^2

f(x) = (x+2+x-2)(x+2-x+2)

f(x) = (2x)(4)

f(x) = 8x

This shows f(x) is a straight line through the origin with slope 8.

Now consider f(x-2):

f(x-2) = 8(x-2) = 8x - 16

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.