Question

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

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

Answer 1

The function is a composition and multiplication of continuous functions, so as long as it is defined, `f` is continuous.

Explanation:

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 >=0`, or equivalently when `x>=-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 >=-6`; in interval notation, in the interval `[-6, +oo)`