AP

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

Problem

Define

h:\mathbb R\to \mathbb R

h(x)=\dfrac{1}{|x-2|+1}

. (i) Find the domain of

h

. (ii) Determine the range of

h

. Give your answer in interval notation. (iii) Draw a neat, labelled sketch of

y=h(x)

, clearly indicating any intercepts, asymptotes, and turning points.