# Continuous function

## Homework Statement

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)

## 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

## Answers and Replies

Dick
Science Advisor
Homework Helper
You are absolutely right. A piecewise continuous function is continuous on the interior of each of the pieces, a continuous function is continuous everywhere.

HallsofIvy
Science Advisor
Homework Helper
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".

Dick
Science Advisor
Homework Helper
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".

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