Which of the following sketches is a graph of \(x^4y^2=2y+1\)?




The equation rearranges to \[x^4 = y^2 + 2y + 1 = (y+1)^2\] which is true if and only if \[x^2=y+1 \qquad \text{or} \qquad x^2=y+1.\]
So the graph consists of two parabolae, \(y=x^21\) and \(y=x^21\), which both cross the \(y\)axis at \(y=1\), and so form the graph in (b).