Question

find and sketch the domain of the function in 3D:
f(x,y) = sqrt(x*y)

Answer 1

@jim_thompson5910

Answer 2

so far all I got is x*y cannt be less than 0

Answer 3

correct

Answer 4

xy < 0 means that either x < 0 or y < 0

Answer 5

if both x < 0 AND y < 0, then xy > 0

Answer 6

so you just have to make sure that either

case 1) both x and y are positive (or zero)

OR

case 2) both x and y are negative (or zero)

Answer 7

i need to sketch it :/

Answer 8

@jim_thompson5910
do you know how to sketch it in 3D?

Answer 9

@AlexandervonHumboldt2

Answer 10

im having trouble understanding how to sketch functions in 3D

Answer 11

without software, I think it's going to be a real pain to sketch in 3D

Answer 12

hopefully you can use a computer tool?

Answer 13

nope

Answer 14

i found what it's supposed to look like online but it's such a wierd shape lol

Answer 15

well I guess you could think of either x or y to be constant while the other is a variable

Answer 16

so for instance, let y be fixed to y = 2

sqrt(x*y) = sqrt(x*2) = sqrt(2x)