CÓMO GRAFICAR UNA FUNCIÓN RACIONAL

How to Graph a Rational Function

Introduction to Graphing Rational Functions

• The video begins with an introduction by Julián, who will demonstrate how to graph a rational function. He mentions that the focus will be on the graphical representation rather than calculating asymptotes and intersections.

Identifying Asymptotes

• Julián explains the process of drawing vertical and horizontal asymptotes. The vertical asymptote is located at x = -1.25 , which he marks on the graph.

• The horizontal asymptote is identified at y = 0.66 . This value is approximated between 0 and 1 on the graph.

Finding Intersections with Axes

• The intersection with the x-axis occurs at x = -0.5 . Julián indicates this point on the graph.

• He also identifies the intersection with the y-axis at y = 0.25 , marking it clearly for reference.

Sketching the Function

• Julián describes how to sketch parts of the function based on identified points and symmetry in diagonal sections of the graph.

• He emphasizes that all parts of a rational function must pass through axis intersections and remain parallel to horizontal asymptotes without crossing them.

Key Characteristics of Rational Functions

• Important characteristics include:

• Must intersect axes as calculated.

• Ends must be parallel to horizontal asymptotes, never touching or crossing them.