Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

question 166

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

• A) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } = 25\); range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at \(( 0,0 )\) and radii \(r , 0 < r \leq 5\)
• B) Domain: all points in the \(x y\)-plane; range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at ( 0 , 0 ) and radii \(r , 0 < r \leq 5\)
• C) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: circles with centers at \(( 0,0 )\)
• D) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } \leq 25\); range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at \(( 0,0 )\) and radii \(r , 0 < r \leq 5\)

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