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anonymous

  • one year ago

please help find domain/range of this function f(x)=-sqrt(x+3)

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  1. Vocaloid
    • one year ago
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    well, let's start off w/ the domain everything under the square root (radical) must be greater than or equal to 0, giving us: \[x+3 \ge0\]

  2. anonymous
    • one year ago
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    i understand that... but the negative before the sqrt is what makes me unsureee

  3. Vocaloid
    • one year ago
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    the negative sign doesn't make a difference for domain. it will change the range though

  4. anonymous
    • one year ago
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    then i think its X must be greater than or equal to -3 for domain

  5. Vocaloid
    • one year ago
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    yup! do you think you can find the range now?

  6. anonymous
    • one year ago
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    umm.. no haha.. plug -3 in for x..? :s

  7. Vocaloid
    • one year ago
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    not quite, haha. well, first, let's consider y = sqrt(x+3), without the negative sign for now you would agree that y must be greater than or equal to 0, correct? since square root of anything must be greater than or equal to 0

  8. anonymous
    • one year ago
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    yes id agree

  9. Vocaloid
    • one year ago
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    all the negative sign does is "flips" the graph across the y-axis, making our domain y \[y \le 0\] since all our y values are now negative or 0

  10. Vocaloid
    • one year ago
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    *x-axis

  11. Vocaloid
    • one year ago
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    our graph ends up looking like this: |dw:1440111137663:dw|

  12. Vocaloid
    • one year ago
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    *range

  13. anonymous
    • one year ago
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    so the range would be (-infinity,0)

  14. Vocaloid
    • one year ago
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    almost, (-infinity,0] since 0 is included

  15. Vocaloid
    • one year ago
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    (we use square brackets when we want to include the other value)

  16. anonymous
    • one year ago
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    ohhhh yaaaa, sorry brain fart lol thank you so much

  17. anonymous
    • one year ago
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    @Vocaloid i have another question... what would be the best way to find f(x)=3sinx

  18. Vocaloid
    • one year ago
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    ah, ok, let's start off by looking at f(x) = sin(x) this function has a domain of (-infinity,infinity) and a range of [-1,1] and looks something like this: |dw:1440111869717:dw|

  19. Vocaloid
    • one year ago
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    now, we look at f(x) = 3sin(x), which just stretches the graph by a factor of 3, like so: |dw:1440111923075:dw| so, any ideas about our domain and range?

  20. anonymous
    • one year ago
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    the domain should be (-infinit,infinity)

  21. Vocaloid
    • one year ago
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    right, and the range?

  22. anonymous
    • one year ago
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    [-3,3]

  23. Vocaloid
    • one year ago
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    yuppp good job!

  24. anonymous
    • one year ago
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    praise you math god lol. i might have a few more questions

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