Answer:
Domain: [0, ∞); range: [3, ∞)
Explanation:
1. Describe the two transformations that occur to the parent function f(x)=x√ when transformed to the function g(x)=2x√+3. The correct way in which to write these two functions follows:
Parent function f(x)=√x transformed function g(x)=2√x+3.
First, the graph of the parent function is stretched vertically by a factor of 2. Second, the resulting graph is translated 3 units up.
2. Then, describe the domain and range of g(x). (You may use Interval Notation or Words)
The input (argument) of a square root function must be from [0, ∞). This is the domain of the function g(x).
Note that if x = 0, g(0) = 3. This 3 is the smallest value that g(x) can have. There is no upper limit on g(x). Thus, the range is [3, ∞).