## anonymous one year ago Let A be the set of all functions with domain R and codomain [-1,1]. 1. Give 2 functions that are elements of A. 2. Let R = {(f,g) l f(0) = g(0)}. Determine if the given reflection is reflexive, symmetric, and/or transitive. Give brief explanations to go with your answers. 3. Describe in words the set given by [cosx]. (We did a problem before that defined the set [x] for a given relation R by the rule [x] = {y l (x,y) ∈ R}.)

1. anonymous

since and cosine come to mind right away

2. anonymous

they leave so very quickly...

3. anonymous

Thank you for your help; I really appreciate it. I realized I switched the domain and codomain for part a when I initially tried this.

4. anonymous

for b, does that mean f and g are each a function where their y intercepts are equal?

5. zepdrix

Hmm, ya it seems that way :o

6. anonymous

then it would definitely be reflexive since the same function would have the same points

7. zepdrix

Hmm, I'm not sure if I'm missing something... because showing that it's an equivalence relation almost seems trivial. Transitive: If fRg then we need gRf. So if f(0)=g(0), then g(0)=f(0) is clearly true for any functions in A.

8. zepdrix

Ya reflexive seems to work out clearly as well.

9. anonymous

Thanks :)

10. anonymous

For part c, I assumed the set [cosx] just meant the range [-1,1] of the function.. Is that the way to describe that in words?

11. zepdrix

Hmm I dunno :d the notation is confusing lol.$\large\rm [\color{orangered}{x}]=\{y~|~(\color{orangered}{x},y)\in R\}$Based on the previous exercise they referred to, I guess we have something like this,$\large\rm [\color{orangered}{\cos x}]=\{y~|~(\color{orangered}{\cos x},y)\in R\}$So we need ... words? Like human words for this? Hmmm..

12. zepdrix

This is the set of y values such that cos x is in relation to y. That's how I would read it. So ya, it's uhhh.. the entire range right? as you said? :o

13. zepdrix

there's probably some pretty way to word that >.<

14. freckles

[cos(x)] is the set of functions f with domain all real numbers and codomain [-1,1] and cos(0)=f(0)

15. freckles

it has been a while since I looked at words codomain and range I think the range of the function can actually be a subset of the codomain and they used the word codomain earlier not range

16. freckles

so I think one element of [cos(x)] would be f(x)=1 since cos(0)=f(0)=1 that is just one example what one of the elements I think we would have

17. freckles

also I'm under the assumption we are using the way R was defined in 2...

18. dan815

also circles and ellipses