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logynklode

  • 2 years ago

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

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  1. lgbasallote
    • 2 years ago
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    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
    • 2 years ago
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    4 & 1. would i add them? and its odd?

  3. lgbasallote
    • 2 years ago
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    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
    • 2 years ago
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    so the exponents of x are actually 4, 1 and 0 got it?

  5. logynklode
    • 2 years ago
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    alright

  6. logynklode
    • 2 years ago
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    yeah i get it. so its even?

  7. lgbasallote
    • 2 years ago
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    now, look at 4, 1, 0 <--are these numbers even, odd or neither?

  8. logynklode
    • 2 years ago
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    neither. because 4 even 1s odd

  9. lgbasallote
    • 2 years ago
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    right,

  10. lgbasallote
    • 2 years ago
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    so this polynomial is neither

  11. logynklode
    • 2 years ago
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    great!

  12. logynklode
    • 2 years ago
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    thanks, can you help me with a few more?

  13. lgbasallote
    • 2 years ago
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    sure

  14. logynklode
    • 2 years ago
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    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
    • 2 years ago
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    the exponents in this case are 6, 4 and 2..are those numbers odd?

  16. logynklode
    • 2 years ago
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    true i meant even lol so that an even function

  17. lgbasallote
    • 2 years ago
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    yes

  18. logynklode
    • 2 years ago
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    f(x) = -5x^5 - 4x^3 - 7 woul that be odd?

  19. satellite73
    • 2 years ago
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    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
    • 2 years ago
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    remember, i said constants have x^0 so 7 is actually 7x^0 0 is not odd

  21. logynklode
    • 2 years ago
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    so f(x) = -5x^5 - 4x^3 - 7x ?

  22. logynklode
    • 2 years ago
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    or f(x) = -5x^7 - 4x^5 - 7x^3

  23. lgbasallote
    • 2 years ago
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    both

  24. logynklode
    • 2 years ago
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    both are odd?

  25. lgbasallote
    • 2 years ago
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    yes one has exponents 7, 5, 3 <--all are odd the other is 5,3 ,1 <--all are odd

  26. logynklode
    • 2 years ago
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    okay. so the next question. Use the graph of f to estimate the local maximum and local minimum

  27. logynklode
    • 2 years ago
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  28. lgbasallote
    • 2 years ago
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    don't you just look at the "turning points" of that graph?

  29. logynklode
    • 2 years ago
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    i thought so, but last tiem i got it wrong so i want to double check.

  30. logynklode
    • 2 years ago
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    Local maximum: approx. (-1,1.17); local minimum: approx. (2,-3.33) ?

  31. lgbasallote
    • 2 years ago
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    hmm...i'm not a master of graphs so i'm afraid i'll have to ask help from @helder_edwin

  32. logynklode
    • 2 years ago
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    alright. theres one more. its graphs too tough. but i have choices, maybe that will help?

  33. lgbasallote
    • 2 years ago
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    i think answers from @helder_edwin will be more precise

  34. logynklode
    • 2 years ago
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    alright

  35. logynklode
    • 2 years ago
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    @helder_edwin ?

  36. helder_edwin
    • 2 years ago
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    u r right. u got a local maximum at x=-1 and a local minimun at x=2.

  37. logynklode
    • 2 years ago
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    alright. i have one more. can you let me know if im correct?

  38. helder_edwin
    • 2 years ago
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    fire away.

  39. logynklode
    • 2 years ago
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    Determine the intervals on which the function is increasing, decreasing, and constant

  40. logynklode
    • 2 years ago
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  41. logynklode
    • 2 years ago
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    i got Increasing x > 0; Decreasing x < 0

  42. helder_edwin
    • 2 years ago
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    no. it is increasing over the entire real line

  43. helder_edwin
    • 2 years ago
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    always read a graph from left to right.

  44. logynklode
    • 2 years ago
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    Increasing on all real numbers?

  45. helder_edwin
    • 2 years ago
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    yes.

  46. logynklode
    • 2 years ago
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    thank you!

  47. helder_edwin
    • 2 years ago
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    u r welcome

  48. helder_edwin
    • 2 years ago
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    @lgbasallote thanks for the referral.

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