Claims About a Min-Value Function

Let $f(x)=|x+1|+|ax-2|$ ($a>0$) with domain $\mathbb R$, and let $M(a)$ be its minimum value. Determine, with proof, which of the following claims are true.

1. The minimum value of $M(a)$ is $1$. 2. The maximum value of $M(a)$ is $3$. 3. $f(x)$ is decreasing on $(-\infty,-1)$. 4. There is exactly one value of $a$ for which the graph of $y=f(x)$ has an axis of symmetry perpendicular to the $x$-axis.