jmc

If $x\ge 0,$ then $f(|x|)=f(x).$ And if $x<0,$ then $f(|x|)=f(-x).$ Thus, the graph of $y=|f(x)|$ is obtained by taking the part of the graph of $y=f(x)$ that is to the right of the $y$-axis, and making a copy by reflecting it across the $y$-axis. The correct graph is $\boxed{\text{A}}.$