Answer
$(1,\frac{1}{2})$ and $(-1,\frac{1}{2})$ are located on the graph.
$(1.1)$ is not located on the graph.
Work Step by Step
$\textbf{To determine whether a point is on a line,}$
$\textbf{simply plug the points back into the equation}$.
When we plug in $(1,\frac{1}{2})$ and $(-1,\frac{1}{2})$ into the equation of $y(x^2+1)=1$ as $x$ and $y$ respectively, the equation works out, which indicates that the points are located on the graph.
But when we plug in $(1,1)$ into the equation, the equation is not work out, which indicates that the point is not located on the graph.