To determine the type of parent function that the equation [tex]\( f(x) = \sqrt{x} \)[/tex] represents, we should examine the form and characteristics of the equation.
The given equation is [tex]\( f(x) = \sqrt{x} \)[/tex]. Let's analyze the options provided:
A. Cube Root:
A cube root function has the form [tex]\( f(x) = \sqrt[3]{x} \)[/tex] or [tex]\( f(x) = x^{1/3} \)[/tex]. This form involves taking the cube root of [tex]\( x \)[/tex]. Our function involves a square root rather than a cube root, so this is not the correct choice.
B. Square Root:
A square root function has the form [tex]\( f(x) = \sqrt{x} \)[/tex]. This is the same as our given function. In a square root function, the input [tex]\( x \)[/tex] is under a square root sign. This matches our given equation precisely.
C. Reciprocal:
A reciprocal function typically has the form [tex]\( f(x) = \frac{1}{x} \)[/tex], where the function is the reciprocal of [tex]\( x \)[/tex]. This form is quite different from our given function, so it doesn't match.
D. Absolute Value:
An absolute value function has the form [tex]\( f(x) = |x| \)[/tex], where the function returns the absolute value of [tex]\( x \)[/tex]. This doesn't involve any roots and is not the form of our given function.
Given the analysis, the equation [tex]\( f(x) = \sqrt{x} \)[/tex] represents a Square Root function.
Therefore, the correct choice is:
B. Square Root
