To determine the type of parent function that the equation [tex]\( f(x) = \frac{1}{x} \)[/tex] represents, let's analyze the given function thoroughly.
1. Square Root Function:
- The general form of a square root function is [tex]\( f(x) = \sqrt{x} \)[/tex].
- Clearly, [tex]\( \frac{1}{x} \)[/tex] does not take the form of [tex]\( \sqrt{x} \)[/tex].
2. Reciprocal Function:
- The general form of a reciprocal function is [tex]\( f(x) = \frac{1}{x} \)[/tex].
- The given function [tex]\( f(x) = \frac{1}{x} \)[/tex] exactly matches this form.
3. Absolute Value Function:
- The general form of an absolute value function is [tex]\( f(x) = |x| \)[/tex].
- Again, [tex]\( \frac{1}{x} \)[/tex] does not take the form of [tex]\( |x| \)[/tex].
4. Cube Root Function:
- The general form of a cube root function is [tex]\( f(x) = \sqrt[3]{x} \)[/tex].
- The given function [tex]\( \frac{1}{x} \)[/tex] does not match [tex]\( \sqrt[3]{x} \)[/tex].
By analyzing the forms of different parent functions, we ascertain that [tex]\( f(x) = \frac{1}{x} \)[/tex] is a reciprocal function. Therefore, the type of parent function represented by the equation [tex]\( f(x) = \frac{1}{x} \)[/tex] is:
B. Reciprocal
