5
AssignmentMultiple Choice

Absolute Value Functions and Translations

Question 5 • FL-1200310-Algebra 1 A

The graph of f(x) = |x| is reflected across the x-axis and translated right 8 units. Which statement about the transformed function is correct?

Answer
A
The domain is the same as the parent function’s domain.
B
The graph opens in the same direction as the parent function.
C
The range is the same as the parent function’s range.
D
The vertex is the same as the parent function’s vertex.

Explanation

Reflecting f(x) = |x| across the x-axis gives -|x|, and translating it right 8 units gives -|x - 8|. These transformations change the graph’s direction and vertex, but not its domain: every real x-value is still allowed. Therefore, the domain is the same as the parent function’s domain.

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