Example 1 Try to find the interval of monotonic increase for the function $y=\log _{0.5}\left(x^{2}+4 x+4\right)$.
Solution: From $x^{2}+4 x+4=(x+2)^{2}>0$, we know that the domain of the function is $(-\infty, -2) \cup (-2, +\infty)$.

Let $y=f(u)=\log _{0.5} u, u=x^{2}+4 x+4$. Since $f(u)$ is a monotonically decreasing function on $\mathrm{R}^{+}$, and $u=x^{2}+4 x+4$ is a decreasing function on $(-\infty, -2)$, and an increasing function on $(-2, +\infty)$, it follows from the monotonicity of composite functions that $y=f(x)=\log _{0.5}\left(x^{2}+4 x+4\right)$ is a monotonically increasing function on $(-\infty, -2)$.
In fact, let $x_{1}<x_{2}<-2$.
$$
\begin{aligned}
& \text { Then } u_{1}=x_{1}^{2}+4 x_{1}+4, u_{2}=x_{2}^{2}+4 x_{2}+4, \\
& \text { and } u_{1}>u_{2}>0 .
\end{aligned}
$$
Since $f(u)$ is a monotonically decreasing function, we have $f(u_{1})<f(u_{2})$, which means $f(x_{1})<f(x_{2})$.

Therefore, $f(x)$ is a monotonically increasing function on $(-\infty, -2)$.