# How do you find the domain and range of sqrt(5x-3) + 4?

Dec 23, 2016

The domain is limited by the rule that the argument of a square root must be non-negative.

#### Explanation:

Domain:
$5 x - 3 \ge 0 \to x \ge \frac{3}{5}$ (there is no upper limit)

Range:
The lower limit of $\sqrt{5 x - 3}$ is $0$,
so the range of the function as a whole is $y \ge 4$ (with again no upper limit)
graph{sqrt(5x-3)+4 [-7.57, 24.47, -1.98, 14.05]}