# How do you find the domain and range of f(x)=sqrt(4-x)?

$x \le 4 , y \ge 0$

#### Explanation:

The domain of a function is the set of all allowable $x$ values. What are the allowable values of $x$ in the equation $f \left(x\right) = \sqrt{4 - x}$? Keep in mind that, in general, we don't allow values inside a square root sign to be negative. So our allowable values of $x$ are:

$4 - x \ge 0 \implies x \le 4$

The range of a function is the set of $y$ values associated with the domain. What are the resulting values of $y$? We know that, with $x = 4 , y = 0$ and that is the lowest value of $y$ we'll have. As $x$ increases, $y$ will increase also, albeit far more slowly. And so our range is:

$y \ge 0$