anonymous
  • anonymous
please help find domain/range of this function f(x)=-sqrt(x+3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Vocaloid
  • Vocaloid
well, let's start off w/ the domain everything under the square root (radical) must be greater than or equal to 0, giving us: \[x+3 \ge0\]
anonymous
  • anonymous
i understand that... but the negative before the sqrt is what makes me unsureee
Vocaloid
  • Vocaloid
the negative sign doesn't make a difference for domain. it will change the range though

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anonymous
  • anonymous
then i think its X must be greater than or equal to -3 for domain
Vocaloid
  • Vocaloid
yup! do you think you can find the range now?
anonymous
  • anonymous
umm.. no haha.. plug -3 in for x..? :s
Vocaloid
  • Vocaloid
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
anonymous
  • anonymous
yes id agree
Vocaloid
  • Vocaloid
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
Vocaloid
  • Vocaloid
*x-axis
Vocaloid
  • Vocaloid
our graph ends up looking like this: |dw:1440111137663:dw|
Vocaloid
  • Vocaloid
*range
anonymous
  • anonymous
so the range would be (-infinity,0)
Vocaloid
  • Vocaloid
almost, (-infinity,0] since 0 is included
Vocaloid
  • Vocaloid
(we use square brackets when we want to include the other value)
anonymous
  • anonymous
ohhhh yaaaa, sorry brain fart lol thank you so much
anonymous
  • anonymous
@Vocaloid i have another question... what would be the best way to find f(x)=3sinx
Vocaloid
  • Vocaloid
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|
Vocaloid
  • Vocaloid
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?
anonymous
  • anonymous
the domain should be (-infinit,infinity)
Vocaloid
  • Vocaloid
right, and the range?
anonymous
  • anonymous
[-3,3]
Vocaloid
  • Vocaloid
yuppp good job!
anonymous
  • anonymous
praise you math god lol. i might have a few more questions

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