# How do you find the domain and range of y = sqrt(x-10) + 5?

Refer to explanation

#### Explanation:

Well we have that

$y = f \left(x\right) = \sqrt{x - 10} + 5 =$

since we have a square root the quantity under it must equal or greater than zero hence

$x - 10 \ge 0 \implies x \ge 10$

So the domain is $\left[10 , + \infty\right)$ (where x gets its values)

To find the range eg where y gets its values we notice that

$y - 5 = \sqrt{x - 10} \ge 0 \implies y - 5 \ge 0 \implies y \ge 5$ hence the range is

$\left[5 , + \infty\right)$