Question

What is the domain and rage of the equation below

Answer 1

\[y=\sqrt{4-x ^{2}}\]

Answer 2

Similarly, here:
4-x^2 >=0

Answer 3

do you know what this is?

Answer 4

solve that

Answer 5

I think the domain is \[-2\le x \le2\]

Answer 6

i mean what \(y=\sqrt{4-x^2}\) represents?

Answer 7

Yep

Answer 8

its an equation

Answer 9

i mean if you graph it

Answer 10

SO i have that. Now whats the range?

Answer 11

Its a square root function if you graph it

Answer 12

start with
\[x^2+y^2=4\] a circle centered at the origin with radius 2

Answer 13

solve for
\(y\) you get \(y=\pm\sqrt{4-x^2}\)
since you are only taking the positive part, it is the upper half of the circle with center \((0,0)\) and radius \(2\)

Answer 14

so you can see from the picture (although algebra works as well) that the domain is \(-2\leq x\leq 2\)

Answer 15

And range is 0<=y<=2 as the graph is above x-axis and below the line y=2

Answer 16

got it?

Answer 17

i got that. thank you for just making it easy to understand lol.

Answer 18

WElcome