Question

Which is true about the domains and ranges of the functions f(x) = 1/8sqrt(x) and g(x) = 8sqrt(x)?

They have the same domain and range.
They have different domains and different ranges.
They have the same range but different domains.
They have the same domain but different ranges.

Answer 1

They have the same domain and range

Explanation:

they're both in the first quadrant

Answer 2

They have the same domain and range.

Explanation:

Since both are derived from the parent graph f(x) = √x, we know that the domain of the parent graph is [0, ∞) and the range is also [0, ∞). Since both graphs are only being modified by vertical stretch/shrink, they still have the same domain and range as the parent graph. Therefore, both graphs have the same domain and range.