The graph of $y=f(x)$ is shown in the $xy$-plane. The graph is a piecewise linear function that resembles a 'W' shape. It crosses the $x$-axis at four distinct points: $(-3,0)$, $(-1,0)$, $(1,0)$, and $(3,0)$.

For how many distinct values of $x$ does $f(x)=0$?