Maria Gaetana Agnesi was a famous 18th century mathematician who published the first complete book on differential and integral calculus. The book featured a famous function that would then receive the name of "the witch of Agnesi".

We are going to try to represent the witch of Agnesi, which has the following equation.

$$f : y = \frac{125}{x^2 + 25}$$

a) To do so, we must complete the following data table first (with just two decimals):

$$\begin{array}{|c|c|} \hline x & \ \ \ y \ \ \ \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 5 & \\ \hline 10 & \\ \hline 20 & \\ \hline 100 & \\ \hline -1 & \\ \hline -2 & \\ \hline -5 & \\ \hline -10 & \\ \hline -20 & \\ \hline -100 & \\ \hline \end{array}$$

b) Now, represent it.

c) Study the function in the graph. Is it symmetrical? For what value of x does it reach its maximum? And what about its minimum? Do you think that it will cross the OX axis or that it will take negative values? Why? What is the interval of growth? What is the interval of decrease?