Continuous Function Homework: Determine & Sketch

[kieranl]

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 doesn't equal the left hand limit. But I am not sure wat the difference is between a continuous function and a piecewise continuous function?

thanks for any help

 

[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.

 

[HallsofIvy]

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]

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.