Charlotte Angas Scott (1858-1931)  was the first mathematician who taught at the women's college Bryn Mawr in the United States. This Pennsylvania college was the first to offer free university education to women, thus helping many girls to enter the world of mathematics. 

One of Charlotte's most important publications was Cartesian Plane Geometry: Analytical Conics.

A conic section is the intersection of a cone and a plane.

If the plane intersects two cones attached at the vertex (double-napped cone) and is not parallel to the generatrix of the cone, a hyperbola with two branches is obtained.

As you know, the graphic representation of the inverse proportionality functions and some rational functions creates hyperbolas.

1- Obtain the graphic representation of the following rational functions:

$$\mathit{a})\quad y = \frac{4}{x - 2} \qquad \mathit{b})\quad y = \frac{2x}{x + 3}$$