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

Question

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

vocaloid · Answer

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 · Answer

i understand that... but the negative before the sqrt is what makes me unsureee

vocaloid · Answer

the negative sign doesn't make a difference for domain. it will change the range though

anonymous · Answer

then i think its X must be greater than or equal to -3 for domain

vocaloid · Answer

yup! do you think you can find the range now?

anonymous · Answer

umm.. no haha.. plug -3 in for x..? :s

vocaloid · Answer

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 · Answer

yes id agree

vocaloid · Answer

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 · Answer

*x-axis

vocaloid · Answer

our graph ends up looking like this:

|dw:1440111137663:dw|

vocaloid · Answer

*range

anonymous · Answer

so the range would be (-infinity,0)

vocaloid · Answer

almost, 

(-infinity,0]

since 0 is included

vocaloid · Answer

(we use square brackets when we want to include the other value)

anonymous · Answer

ohhhh yaaaa, sorry brain fart lol
thank you so much

anonymous · Answer

@Vocaloid i have another question... what would be the best way to find f(x)=3sinx

vocaloid · Answer

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|