Consider the function

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

Problem

f(x)=\dfrac{1}{x}

. Answer the following questions. (i) State the domain and the range of

f

. Give reasons for your answers. (ii) What value does

f(x)

approach when

x

tends to

0

from the right and from the left? What value does

f(x)

approach as

x

tends to

+\infty

and

-\infty

? (iii) Identify the quadrants in which the graph of

f

lies. Explain how the sign of

x

determines the sign of

f(x)