Continuous function

1. May 20, 2009

kieranl

1. The problem statement, all variables and given/known data

Determine whether the function is continuous, piecewise continuous or neither on the segment [0, 10] and sketch the graph of f(t).

f(t)= {10-t, 0<=t<=8 and 10, 8<=t<=10)

3. The attempt at a solution

I would say that it was neither as the right hand limit at t = 8 doesnt equal the left hand limit. But im not sure wat the difference is between a continuous function and a piecewise continuous function???

thanks for any help

2. May 20, 2009

Dick

You are absolutely right. A piecewise continuous function is continuous on the interior of each of the pieces, a continuous function is continuous everywhere.

3. May 21, 2009

HallsofIvy

Staff Emeritus
No, Dick, NOT "absolutely right". That function is equal to 10- t for $0\le t\le 8$ and 10 for $8\le t\le 10$ so it is continuous on the interior of each of those intervals and is "piecewise continuous", not "neither".

4. May 21, 2009

Dick

Right. I only saw that 'the limit doesn't exist' and missed the 'neither'. Thanks.