Which of the following is the set of all real numbers x which there are points on the graph

Question

y=sqrt(-x² ) in the xy plane?

A) The EMPTY SET

B)The set containing only zero

C)The set of all positive real numbers

D)The set of all negative real numbers

E)The set of all real numbers

Answer 1

y=√(-x²)

A)The empty set, only if all other options don't work

B)The set containing only zero, plug 0 into the equation for x and check if you get a real answer.

y=√(-(0)²)

y=√(-(0)√)

y=√(0)

y=0

This could be the answer if no other options work

C)The set of all positive real numbers, choose a positive number to plug in for x and check the solution. I'll plug in 2 to make it easy to work with and avoid some of the complications plugging in 1 can make.

y=√(-(2)²)

y=√(-(4))

y=√(-4)

not a real solution

C is not the answer and neither is E because for E to be the answer, any number plugged in would work.

D)The set of all negative real numbers, the same as above I will plug in -2.

y=√(-(-2)²)

y=√(-(4))

y=√(-4)

not a real solution

D is not the answer

E) As stated above, all of the other options would have to work in order for this to be the answer.

Since B did give a real number as an answer, that is the correct option.

If B did not give a real number the A would be correct.

B