# How do you describe the interval(s) on which the function is continuous, using interval notation?

## f(x) = x sqrt (x + 6)

The function is a composition and multiplication of continuous functions, so as long as it is defined, $f$ is continuous.
The function $f$ is defined for all values $x$ such that the expression inside the square root is non-negative, that is when $x + 6 \ge 0$, or equivalently when $x \ge - 6$. Within that domain, $x + 6$ is a continuous function, the square root is a continuous function and the multiplication by $x$ is also continuous.
Then, $f$ is continuous for all $x \ge - 6$; in interval notation, in the interval $\left[- 6 , + \infty\right)$