Function

[muin]

Let A ⊂ {0, 1, . . . , 9} be a set and ??⊂? be the subset of all even numbers in the set A. Consider a concrete function ?:[−10,10]→? of your choice with the following properties:
– ?(−10)=1=?(10)f(−10)=1=f(10)
– ?f is continuous everywhere except at ??
– ?f is differentiable everywhere except at A

I need to draw a graph and define F

 

[Deleted member 4993]

View attachment 18230
Let A ⊂ {0, 1, . . . , 9} be a set and ??⊂? be the subset of all even numbers in the set A. Consider a concrete function ?:[−10,10]→? of your choice with the following properties:
– ?(−10)=1=?(10)f(−10)=1=f(10)
– ?f is continuous everywhere except at ??
– ?f is differentiable everywhere except at A

I need to draw a graph and define F

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

View attachment 18230
Let A ⊂ {0, 1, . . . , 9} be a set and ??⊂? be the subset of all even numbers in the set A. Consider a concrete function ?:[−10,10]→? of your choice with the following properties:
– ?(−10)=1=?(10)
– ? is continuous everywhere except at ??
– ? is differentiable everywhere except at A

I need to draw a graph and define F

You've shown some work, but you need to explain and complete it. Above, I've removed some duplication that resulted from pasting from your source without checking. You also need to be consistent; when you say "define F", do you mean f or something else? (Names in algebra are case-sensitive.) Isn't what you attached a (partial) definition of f?

I'd like you to first state what your A is; it looks like it may be {0, 1, 2, 3, 4}; then your Ac is {0, 2, 4}. Is that right? So you've tried to make a function that is continuous everywhere except at {0, 2, 4}, and differentiable everywhere except at {0, 1, 2, 3, 4}. Can you demonstrate that this is true, or correct your f so that it is? Don't forget also to define it for 3<=x<=10.

Now you ask about drawing the graph. I would expect you do be doing that as you write the definition of x. Please show what you have tried there, or tell us where you are stuck in graphing.