How do you graph the equation by plotting points y = 1/(1 + x^2)?

You make a list of $x$-values and the corresponding $y$-values.
The points will be all $\left(x , y\right)$ combinations you calculated.
Notice that $x$ is only in ${x}^{2}$ form, so the negative values of $x$ will give the same result as the positive. In other words, the graph is symmetrical with $x = 0$ as axis of symmetry.
Maximum will be at $\left(0 , 1\right)$ and $y = 0$ is the horizontal asymptote