# What is the domain and range for y=-2sqrt(9-3x) +1?

May 17, 2015

The domain is (-oo;3) and the range is (-oo;+1>

The domain is the subset of $\mathbb{R}$ for which the function value can be calculated.
In this function the only restriction for the domain is that $9 - 3 x \ge 0$, because you cannot take square root of negative numbers (they are not real). After solving the inequality you get the domain (-oo;3)

To calculate the range you have to look at the function. There are such things in it:

1. square root of a linear function
2. multiplying by $- 2$
3. adding one to the result

The first mentioned function has a range of <0;+oo)
The action in 2) changes the sign of the result, so the range changes to (-oo;0>
The last action moves the range 1 unit up, so the upper boundary changes from $0$ to $1$