Question

For the given function, complete parts (a) through (f) below. f(x,y) = -(22+272) (a) Find the function's domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is all points (x,y) satisfying (Simplify your answer. Type an inequality.) OB. The domain is the entire xy-plane (b) Find the function's range. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The range is (Type your answer in interval notation) OB. The range is all real numbers c) Describe the function's level curves. Choose the correct answer below. O A. The level curves are parabolas of the form y = cx?. OB. The level curves are ellipses centered at the origin. O C. For f(x,y) = 1, the level curve is the origin. For f(x,y) #1, the level curves are circles centered at the origin. OD. For f(x,y) = 0, the level curve is the x- and y-axes. For f(x,y)#0, the level curves are hyperbolas with the x- and y-axes as asymptotes. (d) Find the boundary of the function's domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The boundary is (Simplify your answer. Type an equation) O B. There are no boundary points. (e) Determine if the domain is an open region, a closed region, or both. Choose the correct answer below. O A. The domain is both open and closed. OB. The domain is closed. O C. The domain is open

Answer 1

- (2x+244) f (x,y) =e function defined Now f is defined everywhore or for R². Domain is whore Domain is entire sy planer f = e-(2x²+242) >o sina for ny t R² Range ; - Range € 60,oo) e .-(22²7 292) -(2x + 2y") = hic © het f=c .lnc en (e?+y) = 2 circles. x + y2 = 0 = (, y) = (0,0) origin. for c=1 the level curves are circles centered at chare is origin for (2,4) #1 For f(ny)=1 level is entire Domain Domain. Boundary of ny plane, boundary points. Sinu open region entire ny plane