How do you find the domain and range of #sqrt( x- (3x^2))#?
The argument of the square root must be greater than or equal to 0:
Becuase this quadratic is the equation of a parabola that opens downward we know that, if we find the roots of the quadratic, the quadratic will be greater than 0 between the roots.
This gives us the domain
We know that the minimum for the range occurs at either root:
We know that the maximum for the range will occur halfway between the roots,
This makes the range become