Question

which of the following would be an example of a function with a range (-infinity a] and a domain [b,infinity) where a > 0 and b > 0

Answer 1

f(x)= √(x-a) +b

Explanation:

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