A family of functions is defined by

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

G_{k}(x)=\dfrac{x^{2}-4}{x-k}

, where

k

is a real parameter. (i) For which value(s) of

k

does

G_{k}(x)

represent a polynomial function? Give reasons. (ii) When

k=2

, state the domain of

G_{2}(x)

and decide whether

G_{2}(x)

is a polynomial or a rational function. (iii) For

k\neq 2

, find the excluded value(s) of

G_{k}(x)

and comment on the nature of discontinuity at those point(s).