Consider the real–valued function

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

Problem

f(x)=\dfrac{1}{x},\;x\neq0

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

f

. (2) (ii) Give a clear reason why the graph of

f

can never meet either coordinate axis. (2) (iii) Describe the behaviour of

f(x)

x\to0^{+},\;x\to0^{-}

and as

|x|\to\infty

. (3) (iv) Into how many separate branches is the graph split? Specify the quadrant(s) in which each branch lies and justify your answer. (3)