To determine the type of parent function for [tex]\( f(x) = \sqrt{x} \)[/tex], let's break down the function step-by-step.
1. Identify the Component: The function [tex]\( f(x) = \sqrt{x} \)[/tex] contains a square root operation.
2. Understand Each Option:
- Reciprocal: A reciprocal function generally has the form [tex]\( f(x) = \frac{1}{x} \)[/tex].
- Cube Root: A cube root function typically looks like [tex]\( f(x) = \sqrt[3]{x} \)[/tex] or [tex]\( f(x) = x^{1/3} \)[/tex].
- Quadratic: A quadratic function usually appears as [tex]\( f(x) = x^2 \)[/tex].
- Square Root: A square root function is represented as [tex]\( f(x) = \sqrt{x} \)[/tex].
3. Match the Function to the Type:
- The given function [tex]\( f(x) = \sqrt{x} \)[/tex] involves taking the square root of [tex]\( x \)[/tex].
By analyzing these points, it is clear that the function [tex]\( f(x) = \sqrt{x} \)[/tex] aligns perfectly with the description of a square root function.
Therefore, the correct answer is:
D. Square root
