# How do you find the intervals on which the function is continuous given  y = sqrt(5x + 9)?

Jul 20, 2018

$x \in \left(- 1.8 , \infty\right)$

#### Explanation:

The square root function cannot work with negative inputs. Therefore, we need to think about when the argument becomes negative. This is simple algebra:

$5 x + 9 < 0$
$5 x < - 9$
$x < - 1.8$

So for any input $x < - 1.8$, this function is undefined. However, for any input greater than that the function is well defined, so it's continuous on that interval.