What is the domain and range of #y=sqrt( x- (3x^2))#?
First, we'll find the range. (it's easier in this problem)
Since the square root radical is already present, we can say right out of the gate that the range is
Next, we'll find the domain.
Since you can't take the square root of a negative number, (over the set of real numbers) we'll see what values of
Just to make it prettier, we'll multiply both sides by negative 1. It makes the coefficient of the squared term positive. Because we are multiplying by a negative, we'll also have to flip the inequality.
We factor out an
However, now we have to use critical number analysis. We'll test various values of
To find critical numbers, we just use the values of
Since we want the number to be less than or equal to zero, we want only one of the two multiplied things (
To start, we'll test a value of
Next, we'll try a value of
Lastly, we have to try a value greater than both critical numbers,
That means that our output will be positive, and therefore greater than zero. It does not work as a solution.