Question

The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 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

Both the domain and range are the same as the parent function.

Reason: reflecting |x| across the y-axis does nothing (|−x| = |x|). Translating left 5 gives g(x) = |x + 5|, which still has domain (−∞, ∞) and range [0, ∞) (minimum 0 occurs at x = −5).