You are Here: Home >< Maths

# continuous funtions.. watch

1. 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?
2. 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

Edit: Are you by any chance a DotA player ?
3. ah right so if the graphs connect they are then continuous, but if they dont then they aren't?

and what is DotA? :P
4. (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
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
5. haha nope, my initials areLDG

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 10, 2010
Today on TSR

### Tuition fees under review

Would you pay less for a humanities degree?

### Can I get A*s if I start studying now?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE