Algebra II (Intermediate Algebra) Season 1 Episode 28 An Introduction to Rational Functions

Algebra II (Intermediate Algebra) is a show focused on teaching concepts and principles of algebra, from basic operations to advanced topics. Season 1 episode 28, entitled "An Introduction to Rational Functions," explores the concept of rational functions and their applications.

The episode begins with an overview of functions and their properties, including domain and range, and how they can be represented graphically. The host explains that rational functions are a specific type of function that involve fractions of polynomials. They are often used in applications involving rates, percentages, and proportions.

The host then goes on to define the key parts of a rational function: the numerator and denominator polynomials, and the vertical and horizontal asymptotes. The numerator is the polynomial in the top of the fraction, and the denominator is the polynomial in the bottom. The vertical asymptote is a line that the function approaches but never crosses, and the horizontal asymptote is a line that the function approaches as the input values become very large or very small.

Next, the host demonstrates how to simplify rational functions by factoring the numerator and denominator, and then canceling out any common factors. They explain that simplifying the function can make it easier to analyze and graph.

The episode then explores how to graph rational functions using techniques such as finding intercepts, asymptotes, and end behavior. The host shows how to use a table of values to plot points, and how to use the behavior of the function at the asymptotes to determine the overall shape.

After demonstrating how to graph a few examples, the episode moves on to applications of rational functions. The host explains how they can be used to model real-world situations, such as population growth or the spread of a disease. They show how to set up and solve equations involving rational functions, and how to interpret the results in the context of the problem.

Finally, the episode concludes with a review of the key concepts covered, including how to simplify and graph rational functions, and how to apply them to real-world situations. The host encourages viewers to continue practicing and exploring the world of rational functions.

Overall, "An Introduction to Rational Functions" is a comprehensive and accessible overview of the topic, suitable for students in Algebra II or anyone interested in learning more about this important concept. The episode provides clear explanations, numerous examples, and practical applications, all presented in a friendly and engaging manner.