## mathmath333 one year ago Graphical functions

1. mathmath333

\large \color{black}{\begin{align} &a.) \ f(x)=-f(x) \hspace{.33em}\\~\\ &b.) \ f(x)=f(-x) \hspace{.33em}\\~\\ &c.) \ \normalsize \text{neither even nor odd function} \hspace{.33em}\\~\\ &d.) \ f(x)\ \normalsize \text{doesn't exist at atleast one point of the domain.} \hspace{.33em}\\~\\ \end{align}}

2. mathmath333

|dw:1435416879315:dw|

3. amoodarya

it is not ? $f(x)=cotan(x)$ because of vertical retricemptotes ,and roots

4. mathmath333

i don't have any clue about the equation of the graph

5. amoodarya

vertical asymptote ! i had a mistake if f(x)=cotan(x) $f(-x)=\cot(-x)=\frac{\cos(-x)}{\sin(-x)}=\frac{\cos(x)}{-\sin(x)}=-\cot(x) =-f(x)$

6. mathmath333

|dw:1435417311725:dw|

7. amoodarya

it looks : the roots have a symmetry I think they show roots ,nothing more if they are part of figure , this is not a function

8. amoodarya

9. phi

btw, choice a) f(x)=-f(x) probably should read f(x) = - f(-x) f(x)= -f(x) would mean y=-y which is only true for y=0

10. mathmath333

m confused is the answer d.)

11. amoodarya

domain of this function has not 1 point out R in your picture ,$D_f=\mathbb{R} -\left\{ 0,a,b \right\}$

12. mathmath333

what is a and b

13. alekos

i'd say the lines just indicate zero crossing points and vertical asymptotes

14. triciaal

From a textbook this is the graph of y = cot x the domain of the secant function is the set of all real numbers except those of the form 1/2 pi + n pi, and the function is continuous on its domain. Because with limit sec x = +/- angle, the graph of the secant function has the lines x = 1/2 pi + nr as vertical asymptotes. There is no intersection of the graph with the x axis because sec x is never zero. The secant function is even because

15. triciaal

|dw:1435422150442:dw|

16. mathmath333

in my book answer is d.)

17. triciaal

and so the graph of the secant function is symmetric with respect to the y axis.

18. amoodarya

|dw:1435418650098:dw|

19. amoodarya

I thin$\pm\pi$k a, b are

20. triciaal

I can see D because it says sec x is never zero no intersection with x axis

21. mathmath333

ok so its d.) , thanks.

22. mathmath333

23. mathmath333

is this even

24. amoodarya

yes , function you draw is even

25. mathmath333

|dw:1435419275045:dw|

26. mathmath333

this graph is even too ?

27. amoodarya

yes I think you tried to sketch sec(x)

28. mathmath333

this is even ?

29. mathmath333

it was not given it is sec x .

30. amoodarya

31. mathmath333

ok thnx

32. mathmath333

what is that dotted line btw

33. amoodarya

vertical asymptote

34. amoodarya

do you know vertical asymptote ?

35. mathmath333

yes

36. mathmath333

not in graph

37. amoodarya

usually when denominator goes to zero , function go to infinity (usually)

38. amoodarya

now , whats your choice ?

39. mathmath333

choice ?

40. amoodarya

a,b,c,d ?

41. mathmath333

b.)

42. mathmath333

i mean it is even function

43. amoodarya

it is not an even function in your picture I see a odd function

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