Consider the reciprocal function defined for all real
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the reciprocal function f(x)=x1 defined for all real x=0. Answer the following questions.
(i) State the domain and the complete range of f.
(ii) Explain, with reference to the behaviour of the graph as x→±∞, why y=0 cannot belong to the range.
(iii) If the domain is restricted to x<0, describe the resulting range and justify your answer.
(iv) If instead the domain is restricted to x>0, describe the resulting range and give reasons for your conclusion.