Question

Which statement best describes g (x) = RootIndex 3 StartRoot x + 6 EndRoot minus 6 and the parent function f (x) = RootIndex 3 StartRoot x EndRoot ?


The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.

Answer 1

The second statement. g(x) = ∛(x+6) − 6 is just f(x) = ∛x shifted left 6 and down 6. Since f has domain (−∞, ∞) and range (−∞, ∞), g also has domain (−∞, ∞) and range (−∞, ∞).