To determine the type of parent function for \( f(x) = \sqrt{x} \), we need to recognize and categorize the defining characteristics of this function.
A parent function defines the simplest form of functions in the same family. Here, we're given \( f(x) = \sqrt{x} \).
Let's examine each option provided:
A. Cube root: This would represent functions of the form \( f(x) = \sqrt[3]{x} \). Clearly, \( \sqrt{x} \) and \( \sqrt[3]{x} \) are different because the cube root involves raising a number to the power of \( \frac{1}{3} \) rather than \( \frac{1}{2} \).
B. Reciprocal: Functions in this family typically take the form \( f(x) = \frac{1}{x} \). This is different from \( \sqrt{x} \), which involves taking the square root.
C. Square root: This function directly involves taking the square root of \( x \), written as \( f(x) = \sqrt{x} \). This matches exactly what we were given.
D. Quadratic: This represents functions like \( f(x) = x^2 \), involving squaring \( x \). This does not match \( f(x) = \sqrt{x} \), where we take the square root instead.
Given that \( f(x) = \sqrt{x} \) matches exactly with option C, the correct answer is:
C. Square root
