Answer:
Closed and Bounded.
Step-by-step explanation:
Hi there!
1) Let's start by finding the values in which the function is defined. Remember that this can be rewritten:
![f(x,y) = 1 + (4 -y^2)^{\frac{1}{2}} \:id\:est\:f(x,y)=1+\sqrt{(4 -y^2)}](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%201%20%2B%20%284%20-y%5E2%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%3Aid%5C%3Aest%5C%3Af%28x%2Cy%29%3D1%2B%5Csqrt%7B%284%20-y%5E2%29%7D)
Since every quadratic root are defined for values
0 then, this help us to understand that we need calculate what interval this Domain is:
![4-y^{2} \geq 0\\4-y^{2}-4\geq -4\\-y^{2}\geq-4 \\y^{2}\leq4\\-2\leq y\leq 2](https://tex.z-dn.net/?f=4-y%5E%7B2%7D%20%5Cgeq%200%5C%5C4-y%5E%7B2%7D-4%5Cgeq%20-4%5C%5C-y%5E%7B2%7D%5Cgeq-4%20%5C%5Cy%5E%7B2%7D%5Cleq4%5C%5C-2%5Cleq%20y%5Cleq%202)
![D=[-2,2]](https://tex.z-dn.net/?f=D%3D%5B-2%2C2%5D)
2) Graphically speaking, the domain is closed. For the values -2 and 2 are included, and bounded.
Bounded functions have all of their points contained by some circle origin centered. Check it out below.
Number seven is a right angle