Continuous Function Homework: Determine & Sketch

Click For Summary

Homework Help Overview

The problem involves determining the continuity of a piecewise function defined on the interval [0, 10]. The function is given as f(t) = {10-t, 0<=t<=8 and 10, 8<=t<=10}. Participants are tasked with assessing whether the function is continuous, piecewise continuous, or neither, and to sketch its graph.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • One participant suggests that the function is neither continuous nor piecewise continuous due to limits at a specific point. Others question the definitions of continuous and piecewise continuous functions, leading to a discussion about the nature of continuity in piecewise functions.

Discussion Status

There is an ongoing debate regarding the classification of the function. Some participants provide clarifications on the definitions of continuity, while others express uncertainty about the implications of limits at the boundary of the piecewise segments. No consensus has been reached, but there is an exchange of ideas regarding the function's properties.

Contextual Notes

Participants are navigating the definitions of continuity and piecewise continuity, with some confusion about the limits at the transition point of the piecewise function. The discussion reflects a need for clarity on these concepts without resolving the underlying questions.

kieranl
Messages
22
Reaction score
0

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
 
Physics news on Phys.org
You are absolutely right. A piecewise continuous function is continuous on the interior of each of the pieces, a continuous function is continuous everywhere.
 
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".
 
HallsofIvy said:
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.
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
4
Views
4K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K