jmc

When the graph $y=f(x)$ is shifted $2$ units to the right, the result is a graph of $y=f(x-2)$; when it is then stretched vertically by a factor of $2$, the result is a graph of $y=2f(x-2)$. Therefore, our information about $f(x)$ can be rendered as an equation: $$f(x)=2f(x-2).$$Applying this equation five times, we get $$\begin{array}{rl}f(10)& =2f(8)\\ & =4f(6)\\ & =8f(4)\\ & =16f(2)\\ & =32f(0)\\ & =\boxed{3.2}.\end{array}$$