What are the asymptote(s) and hole(s), if any, of # f(x) = tanx#?

1 Answer
Dec 9, 2017

Answer:

#f(x) = tan(x)# is a continuous function on its domain, with vertical asymptotes at #x = pi/2 + npi# for any integer #n#.

Explanation:

#f(x) = tan(x)#

has vertical asymptotes for any #x# of the form #x = pi/2 + npi# where #n# is an integer.

The value of the function is undefined at each of these values of #x#.

Apart from these asymptotes, #tan(x)# is continuous. So formally speaking #tan(x)# is a continuous function with domain:

#RR "\" { x : x = pi/2+npi, n in ZZ }#

graph{tan x [-10, 10, -5, 5]}