Question

The function h(x) is a transformation of the square root parent function, f(x)=square root of x. What function is h(x)?

O A. h(x) = V2 - 6
O B. h(x) = V0 + 6
O c. h(x) = v= +6
O D. h(x) = -6

Answer 1

When considering transformations of the square root parent function f(x) = √x, option C h(x) = √(x + 6) correctly represents a horizontal shift 6 units to the left of the parent function, making it the transformed function h(x).

Step-by-step explanation:

To solve for the function h(x), we consider the parent function f(x) = √x (the square root of x). To identify the transformation of f(x) represented by h(x), we must look at the operations performed on x and how they affect the original square root function. Looking at the provided options:

• h(x) = √(2 - 6) could imply a horizontal shift, but the correct notation would be h(x) = √(x - 6).
• h(x) = √(0 + 6) doesn't convey a transformation as square roots cannot have negative input for real numbers, and √0 is just 0.
• h(x) = √(x + 6) implies a horizontal shift of 6 units to the left.
• h(x) = -6 represents a constant function, not a square root transformation.

The correct transformation is depicted by option C, where the square root function has been shifted 6 units to the left, resulting in h(x) = √(x + 6).