Sketching a graph that meets given condition

  • #1

Homework Statement


Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible)

- f is continuous on (0,1), takes on only two distinct values.

Homework Equations




The Attempt at a Solution


https://scontent-lga3-1.xx.fbcdn.net/v/t34.0-12/13020084_1115236431831934_1952173744_n.jpg?oh=36c9b39d36f9d87dbfe189161ecdf210&oe=570FDD68

The solutions manual said it is impossible.

What is wrong with this function?
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,317
1,007
  • #3
So, intuitively no, since "i lifted my pen while drawing this function".

I just googled the definition
(i) the function f is defined at a
Yes

(ii) the limit of f as x approaches a from the right-hand and left-hand limits exist and are equal
If a is the point that jumps, is the lim x-> a = 1 (correct?)

(iii) the limit of f as x approaches a is equal to f(a).
Iim x-> a = 1 does not equal f(a)=2, no

I see
 
  • #4
18
0
A continuous function on an interval(in R), should possess an intermediate value property. That's why it's impossible
 
  • #5
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible)

- f is continuous on (0,1), takes on only two distinct values.


The solutions manual said it is impossible.
Whether or not it is possible depends on exactly how the problem's wording is interpreted.
Interpretation (1): f is defined on [0,1] and takes two values on that set. It is continuous on (0,1).
Interpretation (2): f is defined on [0,1]. It is continuous on (0,1) and takes two values on that set.

Interpretation (1) is possible, but Interpretation (2) is impossible, for reasons explained already by others.
 

Related Threads on Sketching a graph that meets given condition

  • Last Post
Replies
6
Views
732
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
10
Views
2K
Top