Mathematics

Problem

The function

g

is defined by

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

for

x\neq2

. a. (a) Locate all real critical points of

g

that lie in its domain. b. (b) Determine the intervals of increase and decrease of

g

on each component of its domain. c. (c) Sketch a rough graph of

y=g(x)

, clearly indicating the nature of each critical point, the vertical asymptote, and the sections where the curve rises or falls.