jmc

Note that the graphs of $y=g(x)$ and $y=h(x)$ are the reflections of the graph of $y=f(x)$ across the $x$-axis and the $y$-axis, respectively. Thus, the original graph intersects these two graphs at its $x$-intercepts and $y$-intercepts, respectively. This is shown in the following picture: Since the original graph has 2 $x$-intercepts and 1 $y$-intercept, we have $a=2$ and $b\ge 1$. Since the original function is not invertible, it $could$ intersect its reflection across the $y$-axis elsewhere than at a $y$-intercept, but the graph clearly shows that it does not, so $b=1$ and $10a+b=10(2)+1=\boxed{21}$.