Maria Gaetana Agnesi, an 18th-century Italian mathematician, worked with "the witch of Agnesi". This curve was discussed by Fermat in 1703. It has been recently established that it is an approximation of the distribution of X-rays and optical rays energy spectrum, as well as dissipated power in high-frequency resonance circuits.

The equation for the curve is:

$$y = \frac{a^3}{x^2+a^2}$$

Draw the graph for the following rational functions:

$$\mathit{a)}\quad y = \frac{1}{x^2+1}\qquad \mathit{b)}\quad y = \frac{8}{x^2+4}\qquad \mathit{c)}\quad y = \frac{27}{x^2+9}$$

They are particular cases for the witch of Agnesi.

Note: Use the following data table for each function.

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & -10 & -8 & -6 & -4 & -2 & \ 0\ & +2 & +4 & +6 & +8 & +10 \\ \hline y \\ \hline \end{array}$$