Consider the function .

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

Problem

Consider the function

H(x)=\dfrac{x^{3}-6x^{2}+11x-6}{x^{2}-5x+6}

. (i) Factor the numerator and the denominator completely. (ii) Hence determine all real numbers that are excluded from the domain of

H(x)

. (iii) Simplify

H(x)

to its lowest terms and classify the simplified expression as a polynomial function or a rational function. (iv) Prove that

H(x)

is continuous at every real number except those excluded in part (ii).