Identify the domain and range and sketch the graph of the function
y=-sqrt-x

- anonymous

Identify the domain and range and sketch the graph of the function
y=-sqrt-x

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- anonymous

\[y=\sqrt{-x}\]

- anonymous

\[y=-\sqrt{-x}\]

- anonymous

you can't take the square root of a negative number , solve \[-x\geq 0\] in one step to get the domain

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## More answers

- anonymous

same domainfor \(y=-\sqrt{-x}\)makes no difference

- anonymous

as for the range, the square root is greater than or equal to zero, so minus the square root will be less than or equal to zero

- anonymous

Ok so the domian would be (-infinity, infinity)?

- misty1212

HI!!

- misty1212

and no

- misty1212

do you know how to solve \[-x\geq 0\] for \(x\)?

- anonymous

No

- misty1212

if not, that is fine, i will show you

- anonymous

Ok thanks

- misty1212

ok change the sign, and flip the inequality

- anonymous

Ok

- misty1212

the math teachers call it "multiply by \(-1\)" or sommat, but you just make it positive and change greater than or equal to to less that or equal to

- anonymous

what @misty1212 said

- anonymous

don't you divide by -1 and flip the sign?

- misty1212

lol multiply by -1, divide by -1, potato potahto

- anonymous

ok so would the domain be -1?

- misty1212

ooooh kay lets go slow

- misty1212

the domain is an interval right? not a number

- anonymous

Yes

- misty1212

the question is, what interval is it
now we know that you cannot take the square root of a negative number, so the input has to be positive right?

- misty1212

the input in this case is \(-x\)
in english we would say that \(-x\) must be greater than or equal to zero
in math write
\[-x\geq 0\]

- misty1212

to solve that for \(x\) change the sign so that it is \(x\) instead of \(-x\) and change the inequality as well

- misty1212

i.e \[-x\geq 0\iff x\leq 0\] and that is your domain

- misty1212

if you want to write it as an interval that works too, call it
\[\huge (-\infty, 0]\]

- anonymous

Ok so what would the range be?

- misty1212

ok again we go slow
the range is all possible outputs
the square root is always greater than or equal to zero
you have a minus sign in front, so that means the range will be all numbers less than or equal to zero

- anonymous

Ok so how would I graph it?

- misty1212

if you want to write it as an interval, write it the same as the domain
in this case they are the same

- misty1212

how to you graph \(y=-\sqrt{-x}\)?

- misty1212

is that the question?

- anonymous

Well I have to sketch the graph of the function

- anonymous

do you know what \(y=\sqrt{x}\) looks like?

- anonymous

No

- anonymous

hmm then you can't really do it
maybe look it up

- anonymous

ok

- anonymous

http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%92%E2%88%9A-x%3F

- anonymous

ok be very careful here

- anonymous

wolfram has given you too much information

- anonymous

where it says "complex valued plot" change it to "real valued plot"

- anonymous

Oh ok thanks

- anonymous

|dw:1440985596594:dw|you should see something like that

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