Domain and Range (1 Viewer)

[Norma.Jean]

Okay I know this might be some really obvious answer and i'm sorry but i haven't done this in quite a bit and my brains gone a bit rusty...if brains can rust... :\

anyway it says state the domain and range for

x squared + y sqaured = 4
And
y= -(square root)1-x(squared)

I hope that makes sense but anyway...thanks

 

[clintmyster]

iight the first one is a circle so the domain is -2 is less than or equal to x which is less than or equal to 2. Same thing for range.
this domain comes about due to the radius of the circle being 2.

as for the other. domain is -1 less than or equal to x which is less than or equal to to 1. bcos of the sqroot, x, cannot be greater than 1 as it will make it a negative root..and yeahh..range is just y is greater than or equal to 0

 

[harryboyles]

1) The equation is a circle with the centre being the origin and the radius = 2
Hence the domain is -2 <= x <= 2
The range is -2 <= y <= 2
2) The function (a semi-circle) has a domain: -1 <= x <= 1 (as you can't get the square root of a negative number)
The range is -1 <= y <= 0

This assumes that you meant y=-(1-x^2)^0.5. If it were y=-1^0.5-x^2 if I took your statement literally, then it would become y=-x^2-1
Always include brackets online to indicate where the square root symbol ends.

 

[ratcher0071]

Okay I know this might be some really obvious answer and i'm sorry but i haven't done this in quite a bit and my brains gone a bit rusty...if brains can rust... :\

anyway it says state the domain and range for

x squared + y sqaured = 4
And
y= -(square root)1-x(squared)

I hope that makes sense but anyway...thanks

1)
x² + y²=4 is a circle with C(0,0) and radius=2

Domain:
{xER: -2 <= x <= 2}
Range:
{yER: -2 <= y <= 2}

 

[bored of sc]

x²+ y² = 4

domain: -2 < x < 2

range: -2 < y < 2

drawing a circle makes this become more apparent

 

[bored of sc]

y= -square root(1-x²)

domain: 1-x² cannot be < 0
1 < x²
x = + 1

sub in x = 0
y = + 1 <---- equation still exists

therefore:
-1 < x < 1 <--- since 0 works for equation

range: -1 < y < 0 since the negative sign makes all answers negative (except 0) but the semi circle stops at y = -1 since it has a radius of 1.