Algebra-2

Question Analysis
This question involves identifying the parent function of a transformed reciprocal function.
The main focus is on recognizing the simplest form of the reciprocal function family from which the given function is derived.

Key Concept Explanation
The reciprocal function family has the parent function , which has two hyperbolic branches and is undefined at .
Transformations such as horizontal shifts (added to x in the denominator) and vertical shifts (subtracted outside the fraction) modify the parent function, but the core structure of a reciprocal of a variable confirms it belongs to this family, with as the parent.

Step-by-Step Solution
Analyze the given function: .Note the reciprocal form (1 divided by a linear expression), which is characteristic of reciprocal functions.
Recall that the simplest reciprocal function (parent) is

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