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Why tan x graph is continuous within its domain and is not continuous out of the domain?
Wiki User
∙ 11y ago
we do not check if a function is continuous or not outside it's domain.
"first, f has to be defined at c."
Tanx is not defined where cosx=0 .ie x=pi/2 , 3pi/2 etc
ill try to help more here.
what domain means is what can you put into a function, whereas range, which i am sure you have heard of as well, just means what you can get out of a function. that being said, lets look further into the graph of tanx. when we do, we see that the graph is discontinuous at pi/2. the reason for this is because tanx is equivalent to sinx/cosx. because of this relationship, when you put pi/2 in for x in sinx/cosx, you end up with cosx=0 which makes your denominator zero, which is undefined, which makes your graph discontinuous. because of that, you cannot put pi/2 in for x in tanx, and since the domain is what you can put into an equation, pi/2 which causes a discontinuity is not included in the domain. basicly, wherever a graph is discontinuous, it wont be included in the domain because you cant put stuff in that will make your graph discontinuous
Wiki User
∙ 11y ago
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