Find and Sketch the Domain of a Function

[cosmos42]

Homework Statement

ƒ(x,y) = √y + √[25-x²-y²]

Homework Equations

Quadratic

The Attempt at a Solution

The expression for f(x,y) is defined as long as x² + y² ≥ 25 and y ≥ 0 because of the square roots we can't have negative numbers. {(x,y) ∈ ℝ² : y ≥ 0 and x² + y² ≥ 25} I'm not sure how I'd represent it graphically.

 

[andrewkirk]

What is the shape of the region of the number plane that satisfies $x^2+y^2\leq 25$?
What is the shape of the region of the number plane that satisfies $y\geq 0$?
What is the shape of the intersection of those two regions?