Practice Test

Question 17 • Mathematics II

The graph of f of x is equal to absolute value of x is reflected across the x -axis and translated to the right 6 units. Which statement about the domain and range of each function is correct?

Answer

The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

Both the domain and range of the transformed function are the same as those of the parent function.

The range of the transformed function is the same as the parent function, but the domains of the functions are different.

Neither the domain nor the range of the transformed function are the same as those of the parent function.

Explanation

The parent function f(x) = |x| has domain all real numbers and range y ≥ 0. Reflecting it across the x-axis and shifting it right 6 units gives −|x − 6|: the horizontal shift keeps the domain as all real numbers, while the reflection changes the range to y ≤ 0. So the domain stays the same but the range is different, as stated in choice A.

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