Question

The function f(x) = √x. It is translated using the rule (x, y) = (x - 6, y + 9) to create A(x). Which expression describes the range of A(x)?

A) y > -9
B) y > -6
C) y > 6
D) y > 9

Answer 1

The range of the translated function A(x) is described by y > 9, as the original square root function f(x) = √x has its range shifted upwards by 9 units due to the translation.

Step-by-step explanation:

The original function given is f(x) = √x, which represents the square root function. When this function is translated using the rule (x, y) = (x - 6, y + 9), it means that every point on the graph of the original function is moved 6 units to the right and 9 units up. Since the square root function has a range of y ≥ 0 (because square roots of real numbers are non-negative), the translated function, which we denote as A(x), will also have its range shifted upwards by 9 units. Therefore, the range of the function A(x) after the translation will start from 9 units above 0, which gives us the new range of y > 9.

To be more specific, the range of A(x) can be described as all y values such that y > 9. This translates to option D) y > 9.