## logynklode 2 years ago Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = -3x4 - 2x - 5

1. lgbasallote

there's a shortcut to knowing...just look at the exponents of *every* x. What are the exponents of every x in this case?

2. logynklode

4 & 1. would i add them? and its odd?

3. lgbasallote

nope. remember: any constant is rewritten as cx^0 for example, 1 can be rewritten as 1x^0 2 can be rewritten as 2x^0 so 5 is 5x^0

4. lgbasallote

so the exponents of x are actually 4, 1 and 0 got it?

5. logynklode

alright

6. logynklode

yeah i get it. so its even?

7. lgbasallote

now, look at 4, 1, 0 <--are these numbers even, odd or neither?

8. logynklode

neither. because 4 even 1s odd

9. lgbasallote

right,

10. lgbasallote

so this polynomial is neither

11. logynklode

great!

12. logynklode

thanks, can you help me with a few more?

13. lgbasallote

sure

14. logynklode

before that, can you give me an example of an odd function? would that be like f(x) = -5x^6 - 4x^4 - 7x^2 ?

15. lgbasallote

the exponents in this case are 6, 4 and 2..are those numbers odd?

16. logynklode

true i meant even lol so that an even function

17. lgbasallote

yes

18. logynklode

f(x) = -5x^5 - 4x^3 - 7 woul that be odd?

19. satellite73

it would be except for the 7, which ruins it the degree of a constant is 0, and 0 is an even number

20. lgbasallote

remember, i said constants have x^0 so 7 is actually 7x^0 0 is not odd

21. logynklode

so f(x) = -5x^5 - 4x^3 - 7x ?

22. logynklode

or f(x) = -5x^7 - 4x^5 - 7x^3

23. lgbasallote

both

24. logynklode

both are odd?

25. lgbasallote

yes one has exponents 7, 5, 3 <--all are odd the other is 5,3 ,1 <--all are odd

26. logynklode

okay. so the next question. Use the graph of f to estimate the local maximum and local minimum

27. logynklode

28. lgbasallote

don't you just look at the "turning points" of that graph?

29. logynklode

i thought so, but last tiem i got it wrong so i want to double check.

30. logynklode

Local maximum: approx. (-1,1.17); local minimum: approx. (2,-3.33) ?

31. lgbasallote

hmm...i'm not a master of graphs so i'm afraid i'll have to ask help from @helder_edwin

32. logynklode

alright. theres one more. its graphs too tough. but i have choices, maybe that will help?

33. lgbasallote

i think answers from @helder_edwin will be more precise

34. logynklode

alright

35. logynklode

@helder_edwin ?

36. helder_edwin

u r right. u got a local maximum at x=-1 and a local minimun at x=2.

37. logynklode

alright. i have one more. can you let me know if im correct?

38. helder_edwin

fire away.

39. logynklode

Determine the intervals on which the function is increasing, decreasing, and constant

40. logynklode

41. logynklode

i got Increasing x > 0; Decreasing x < 0

42. helder_edwin

no. it is increasing over the entire real line

43. helder_edwin

always read a graph from left to right.

44. logynklode

Increasing on all real numbers?

45. helder_edwin

yes.

46. logynklode

thank you!

47. helder_edwin

u r welcome

48. helder_edwin

@lgbasallote thanks for the referral.