# How do you find the domain and range of #sqrt( x- (3x^2))#?

##### 1 Answer

Sep 7, 2017

Given:

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