Question

Which of the following could be an example of a function with a domain [a, infinity) and a range [b, infinity) where a >0 and b>0? Answer choices: A)f(x)= 3√x+a -b B) f(x)= √x-a +b C) f(x)= 3√(x-b) +a D)f(x)= √x+a -b

Answer 1

The correct example of a function with the given domain and range requirements is f(x)= √x-a +b, which starts at x=a and shifts upward by b units.

Step-by-step explanation:

The student's question asks for an example of a function with a domain [0 and b>0. Considering the options given, the correct answer is:

B) f(x)= √x-a +b

This function has a domain starting at x=a, since the square root function is defined for x ≥ a, and the expression inside the square root must be non-negative. The range starts at y=b since adding b to the square root function shifts its values upward by b units. Therefore, for x values at and beyond a, the output of the function will be at and beyond b.

Answer 2

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