Consider the reciprocal function

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

Problem

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

, defined for

x\neq0

. Answer the following questions. (i) State the sign of

f(x)

when

x>0

and when

x<0

. (ii) Using limit notation, write four separate statements describing the behaviour of

f(x)

as: (a)

x\to0^{+}

, (b)

x\to0^{-}

, (c)

x\to+\infty

, (d)

x\to-\infty

. (iii) Explain how the limit statements obtained in part (ii) describe the position of the graph of

y=\dfrac{1}{x}

with respect to the coordinate axes.