jmc

Since $$f(2x+1)=f\left(2\left(x+\frac{1}{2}\right)\right),$$the graph of $y=f(2x+1)$ is produced by taking the graph of $y=f(x)$ and compressing it horizontally by a factor of $\frac{1}{2},$ then shifting it $\frac{1}{2}$ units to the left. The correct graph is $\boxed{\text{A}}.$

In particular, to produce the graph of $y=f(2x+1),$ we do not compress it horizontally by a factor of $\frac{1}{2},$ then shift it 1 unit to the left; the function produced by this transformation would be $$y=f(2(x+1))=f(2x+2).$$