Question

The graph of f(x) = |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?

Both the domain and range of the transformed function are the same as those of the parent function.
Neither the domain nor the 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.
The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

Answer 1

The domain is the same, but the ranges are different.

Explanation: f(x)=|x| has domain (-∞, ∞) and range [0, ∞). The transformed function is g(x) = -|x-6|, which also has domain (-∞, ∞) but range (-∞, 0]. Thus the domain is unchanged and the range is different.