Let , where is a non-zero real constant. For which value(s) of is defined for all…

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

f(x)=\dfrac{x^{2}-kx+k}{x-k}

, where

k

is a non-zero real constant. For which value(s) of

k

f(x)

defined for all real

x

and hence behaves as a polynomial function? (a)

k=1

(b)

k=-1

k

exists (d) All non-zero real numbers