Why is the domain and range of x^2+y^2=1 this answer?

- anonymous

Why is the domain and range of x^2+y^2=1 this answer?

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- anonymous

\[D = {-1\le1 \le1}\]

- anonymous

maybe
\[-1\leq x\leq 1\]

- TuringTest

you mean\[-1\le x\le 1\]what if x=2 ?
what would y be?

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## More answers

- anonymous

\[R = -1 \le y \le 1\]

- anonymous

ohh I meant that

- anonymous

yes you are right, it is the unit circle

- anonymous

I get so confused with domains and ranges D:

- anonymous

like why is it -1 less than or equal to x less than or equal to 1?

- TuringTest

what if \[|y|>1\]what would x be?

- anonymous

i don't know.

- TuringTest

try it with x=2
what would y be?

- anonymous

what do you mean?

- experimentX

can't call it a function though ... it's a closed curve.

- anonymous

I just don't understand why it's greater than or less than.. o.o

- TuringTest

@milliex51 can you solve the above for y ?
an experimX is correct as usual, but that doesn't really matter for what we're talking about

- TuringTest

solve\[x^2+y^2=1\]for \(y\) please :)

- anonymous

\[y = +/- \sqrt{-x}+1\]

- anonymous

-x^2

- TuringTest

not quite...

- anonymous

really?

- anonymous

or do I close bracket the 1 too?

- TuringTest

\[y=\pm\sqrt{1-x^2}\]

- anonymous

ohh..

- TuringTest

\[x^2+y^2=1\]\[y^2=1-x^2\]\[y=\pm\sqrt{1-x^2}\]now what if x=2 ?
what do you get for y ?

- experimentX

now if we redefine it x^2+y^2=1 by
y = sqrt(1-x^2) &
y = -sqrt(1-x^2) on a field of real numbers than ..

- TuringTest

^echo, echo.... :P

- experimentX

TuringTest was thinking exactly same as me

- anonymous

isn't it the same from my answer?
um, x=2 would be y=non real?

- TuringTest

and if y is not real, then x=2 is not in the domain, right?

- anonymous

right.

- TuringTest

what about any \[|x|>1\]?
what will y be?

- anonymous

how do I solve that?

- TuringTest

I asking you if you plug in any number greater than 1 in for x into the formula we have for y, what will y e?

- TuringTest

*what will y be?

- anonymous

i don't know D:

- TuringTest

ok, look at it this way...

- TuringTest

what is under the radical in\[y=\pm\sqrt{1-x^2}\]cannot be negative, right?
otherwise y would be imaginary.
do we agree?

- anonymous

yes, yup.

- TuringTest

so that mean that we have a requirement that\[1-x^2\ge0\]right?

- anonymous

yup. or else it will be undefined

- anonymous

or imaginary

- TuringTest

so solve that requirement for x and you will get your domain

- anonymous

but how? ahhh

- TuringTest

\[1-x^2\ge0\]\[1\ge x^2\]perhaps here is where you get a little confused...\[1\ge x\ge -1\]

- anonymous

ohh.. I transpose the negative x^2

- TuringTest

remember that x^2 is always positive, so all that matters is that\[|x|\le1\]and y will be real

- anonymous

how about when I have to look at a graph?

- anonymous

Like:|dw:1333035682317:dw|

- anonymous

what signs am I going to use? o.o

- TuringTest

|dw:1333035736039:dw|we are saying that x can take on any value in the black region, right?

- anonymous

yes

- TuringTest

assuming it includes the endpoints, what is the most that x can be?

- anonymous

-3 and 4

- TuringTest

good :)
which of those is the maximum value of x ?

- anonymous

4

- TuringTest

right, and this translates mathematically to the statement\[x\le4\]agreed?

- anonymous

why because 4 is greater than or equal to x?

- anonymous

can I read it like that?

- TuringTest

"less-than or equal to"

- anonymous

why is it less than? when 4 is the maximum?

- TuringTest

x is less-than or equal-to 4 is how you can read it...
we agree that x cannot be more than four, so x must me
"less-than or equal-to" 4
think about that until it makes sense to you

- anonymous

that's when I get confused. :(

- anonymous

i know that's how I'll read it

- TuringTest

read what I wrote and think about it
x cannot be more than 4
therefor x is less-than or equal to four
does that make sense?

- anonymous

ohhhh

- anonymous

so x has to be less than or equal to 4 so that it won't exceed 4?

- anonymous

how about for 3?

- anonymous

*-3

- TuringTest

exactly
so what about the minimum value of x ?
what is the least x can be?
-3 right?

- anonymous

yes

- TuringTest

so then we can say
x cannot be less than -3
therefor x is greater-than or equal-to -3
same logic as the other one, but make sure you really understand what I wrote

- TuringTest

brb
in the meantime meditate on this idea:
"x cannot be less than -3"
implies that
"x is greater-than or equal-to -3"

- anonymous

so say <-- -3 are all less than?

- anonymous

since they are smaller?

- TuringTest

so are you saying to write\[x\le-3\]?

- TuringTest

"x cannot be less than -3"
implies that
"x is greater-than or equal-to -3"
is that what the above statement says?

- anonymous

no.

- anonymous

I mean yes

- TuringTest

no\[x\le-3\]means "x less-than or equal-to -3"
but we said that x \(cannot\) be less than -3, so this is not the statement we want
we want to say
"x greater-than or equal-to -3"
how do we write that?

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