Let the function $f$ be defined as follows.

$f(x)=x^3+6x^2+9x+5$

$($a$)$ Determine the interval$($s$)$ in the domain of $f$ on which the function is increasing and the interval$($s$)$ in the domain of $f$ on which the function is decreasing.

Write your answers as an interval or list of intervals. When writing a list of intervals, make sure to separate them with commas and to use as few intervals as possible. Click on "None" if applicable.

Interval$($s$)$ on which $f$ is increasing: $(-,]$

Interval$($s$)$ on which $f$ is decreasing: