Graph –3x2 + 12y2 = 84. What are the domain and range?

2 answers

The domain and range of this graph are:

Domain: All real numbers for x.

Range: All real numbers for y such that y is greater than or equal to -2√7 and less than or equal to 2√7.

To find the range, we need to solve for y:

-3x^2 + 12y^2 = 84

12y^2 = 3x^2 + 84

y^2 = (1/4)x^2 + 7

Taking the square root of both sides, we get:

y = ±(1/2)x√(x/28)

Since the term inside the square root must be positive, we know that x/28 must be positive or zero. Therefore, x can be any real number. We also know that the square root of a positive number is always a real number, so our range is all real numbers for y within the given bounds.
AAAaannndd the bot gets it wrong yet again!
got the range exactly backwards
we need 4y^2 > 28
y^2 > 7
so y > √7 or y < -√7