AP

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

Problem

Define

g: \mathbb R\setminus\{1\}\to\mathbb R

g(x)=\dfrac{x^{2}-1}{x-1}

. (i) Simplify

g(x)

for all permissible values of

x

. (ii) Identify the family of functions to which the simplified expression belongs and justify your choice on the basis of degree and typical graph shape. (iii) Find a suitable value to assign at

x=1

so that the resulting function becomes well-defined on the whole of

\mathbb R

and belongs entirely to the same family. (iv) State the domain and range of the extended function obtained in part (iii).

Related theory

Functions
Algebraic Manipulation
Rational Functions

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