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anonymous

  • one year ago

How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function? The function shifts down 3 units, so the range changes from −1 to 1 in f(x) to −4 to −2 in g(x). The function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x). The function shifts down 5 units, so the range changes from −1 to 1 in f(x) to −6 to −4 in g(x). The function shifts down 5 units, so the range changes from −5 to 5 in f(x) to −10 to 0 in g(x).

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  1. anonymous
    • one year ago
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    @phi @radar @aloud @AutumnRoseT @xavierbo2 @Data_LG2 @mathmate @HWBUSTER00 @hartnn

  2. anonymous
    • one year ago
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    was up

  3. anonymous
    • one year ago
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    help mee?

  4. anonymous
    • one year ago
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    i really d know

  5. anonymous
    • one year ago
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    okay thanks though

  6. anonymous
    • one year ago
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    @mathmate ?

  7. mathmate
    • one year ago
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    @georgia545 @aloud Do you know the range of f(x)?

  8. anonymous
    • one year ago
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    0??

  9. mathmate
    • one year ago
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    |dw:1434724687580:dw|

  10. mathmate
    • one year ago
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    So the range of y=cos(x) is [-1,1] Are you familiar with the interval notation?

  11. anonymous
    • one year ago
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    noo

  12. mathmate
    • one year ago
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    Check this out: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01

  13. anonymous
    • one year ago
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    oh yeah i do i just didnt know that was the name

  14. mathmate
    • one year ago
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    range of y=[-1,1] means the range of y can take any value between -1 and +1.

  15. mathmate
    • one year ago
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    Multiplying y by -5 means stretching the function vertically and flipping it about the x-axis. so y=-5cos(x) has a shape like this: |dw:1434724951272:dw| so what is the range of y=-5cos(x)?

  16. anonymous
    • one year ago
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    (5,-5)?

  17. mathmate
    • one year ago
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    ( and ) means values of the limits are excluded, but don't apply here. Use [-5,5]. Intervals always go from smaller to larger values. Please review the link: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01 Don't skim it. Go through the details. Math is a very precise language because there is no redundance.

  18. mathmate
    • one year ago
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    Yes, [-5,5] is the correct new range.

  19. anonymous
    • one year ago
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    So which answer would it be because in f(x) it was [1,-1] to [5,-5] but thats not an option

  20. mathmate
    • one year ago
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    That's because we have not considered the term -3 yet. g(x) = -5cos(x) -3. So do you know what the term would do? It would cause a vertical translation. -3 means a translation of 3 units in the negative y direction, and +2 means a translation up 2 units. I'll leave you with that. You can post for a check if you want.

  21. anonymous
    • one year ago
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    so it would be a because it went from [1,-1] and shifted down 3 right?

  22. Sachintha
    • one year ago
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    It won't be A. Try again. :)

  23. mathmate
    • one year ago
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    Did you say [-1,1] translated down? Recall we have g(x)=-5cos(x)-3.

  24. mathmate
    • one year ago
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    We agreed it was [-5,5] before translation, didn't we?

  25. Sachintha
    • one year ago
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    @georgia545 Don't look forward for a direct answer. Try to work it out following mathmate's instructions.

  26. anonymous
    • one year ago
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    i thought it started as [1,-1] in f(x) then went to [5,-5] in g(x) ????

  27. Sachintha
    • one year ago
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    The range of function g(x) is [5,-5]. Then it is shifted down 3 units in the negative y direction.

  28. Sachintha
    • one year ago
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    Then the range also changes according to it.

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