Which of the following is a key property of the reciprocal parent function?

A. The function has a vertical asymptote.
B. The function has a horizontal asymptote.
C. The function is symmetric with respect to the origin.
D. All of the above.



Answer :

Final answer:

The reciprocal parent function has key properties including points of passage, asymptotes, and the reciprocal of a reciprocal function.


Explanation:

The key property of the reciprocal parent function is that its graph passes through the points (1,1), (-1,-1), and the origin (0,0). For example, the reciprocal parent function of f(x) = 1/x is g(x) = 1/x.

Moreover, the reciprocal parent function has asymptotes at the lines y = 0 and x = 0. These lines act as restrictions on the function's domain.

Additionally, the reciprocal of a reciprocal function results in the original function. In other words, the reciprocal function of the reciprocal parent function will give the original function back.


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