Answer:
B) f(x)= √(x-a) +b
Step-by-step explanation:
The answer choices suggest the parent function is y=√x. This has a domain and range of [0, ∞). The question asks what function transformations will move the domain to [a, ∞) and the range to [b, ∞).
Function transformations
To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.
To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.
The net effect of these transformations is ...
f(x) = √x ⇒ f(x) = √(x -a) +b . . . . . . matches choice B
