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

Question

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 $r , 0 < r \leq 5$

Quizplus · Accepted Answer

The Answer is D

Find the Domain and Range and Describe the Level Curves f(x,y)=25−x2−y2f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }f(x,y)=25−x2−y2​

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