To match the function [tex]\( f(x) = \sqrt{x} \)[/tex] with its appropriate name, let's examine the characteristics of each type of function given in the options:
1. Constant function: A constant function has the form [tex]\( f(x) = c \)[/tex], where [tex]\( c \)[/tex] is a constant. The value of [tex]\( f(x) \)[/tex] does not change with [tex]\( x \)[/tex]. Since [tex]\( f(x) = \sqrt{x} \)[/tex] changes as [tex]\( x \)[/tex] changes, it is not a constant function.
2. Square root function: The function [tex]\( f(x) = \sqrt{x} \)[/tex] is a classic example of a square root function. It takes the non-negative square root of [tex]\( x \)[/tex]. This matches directly with the given function.
3. Linear function: A linear function has the form [tex]\( f(x) = mx + b \)[/tex], where [tex]\( m \)[/tex] and [tex]\( b \)[/tex] are constants. Since [tex]\( f(x) = \sqrt{x} \)[/tex] is not in this form, it is not a linear function.
4. Identity function: An identity function is of the form [tex]\( f(x) = x \)[/tex], where the output is exactly the same as the input. Since [tex]\( f(x) = \sqrt{x} \)[/tex] is not [tex]\( x \)[/tex], it is not an identity function.
5. Squaring function: A squaring function is of the form [tex]\( f(x) = x^2 \)[/tex], where the output is [tex]\( x \)[/tex] squared. Since [tex]\( f(x) = \sqrt{x} \)[/tex] is not [tex]\( x^2 \)[/tex], it is not a squaring function.
Given the characteristics and definitions of the options, the function [tex]\( f(x) = \sqrt{x} \)[/tex] is best matched with the "square root function".
