Mathematics

Problem

Consider the function

h(x)= \begin{cases} \dfrac{|x|}{x}, & x\neq0,\\ k, & x=0. \end{cases}

Which of the following statements about the continuity of

h

x=0

is correct? a) Continuous if

k=0

b) Continuous if

k=1

c) Not continuous for any real

k

d) Continuous if

k=-1