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continuous funtions..

how do i know by looking at this:

f(x) = cos(x) x<= (less than or equal to) 0,
e^-x x E (0,2],
e^-(x-4) x>2.


that "although this function is defined diffrently in three separate regions it is a continuous function"?

and could you possibly give me an example of one the equations which would not make it continuous?
(edited 13 years ago)
Reply 1
Avatar for bolo156
bolo156
The functions are continuous even though defined differently, because at the ends of the intervals they are defined in the y values are the same (ie the curves touch their ends) and there i suppose the third function should be e^-(4-x) or second e^x
but this is the explanation (see: Cos(0)=1 and e^0=1 and then it increases etc and connects with the third function:P) Example if instead cos(x) you'd pus sin(x) the y value at "less than zero" x would be 0 and e^-x would start at 1 , 1 unit gap there, therefore not continuous

Hope this helps :smile:

Edit: Are you by any chance a DotA player ? :wink:
Reply 2
Avatar for elldeegee
elldeegee
OP
19
ah right so if the graphs connect they are then continuous, but if they dont then they aren't?


and what is DotA? :P
Reply 3
Avatar for bolo156
bolo156
Original post by elldeegee
ah right so if the graphs connect they are then continuous, but if they dont then they aren't?


and what is DotA? :P


yes, pretty much:smile:
And DotA is a game (mod for warcraft III)
and LDG is one of the best competetive dota teams, hence why i asked You, elldeegee :wink:
Reply 4
Avatar for elldeegee
elldeegee
OP
19
haha nope, my initials areLDG :smile:

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