Algebra II (Intermediate Algebra) Season 1 Episode 29 The Algebra of Rational Functions
- TV-PG
- March 4, 2011
- 31 min
In Algebra II season 1 episode 29, titled "The Algebra of Rational Functions," viewers are introduced to a key concept in algebra: rational functions. The episode begins with a review of what a function is and how it can be represented in algebraic notation.
From there, the focus shifts to rational functions, which are functions that can be expressed as a ratio of two polynomial functions. The episode explores some basic properties of rational functions, including their domain and range and the different types of asymptotes they can have.
The episode then delves into how to graph rational functions, including the use of horizontal and vertical asymptotes, and how to identify holes and intercepts in the graph. Viewers will learn how to use a table of values to graph a rational function, as well as how to identify key points on the graph, such as the x and y intercepts.
Throughout the episode, viewers will see examples of different types of rational functions, each with its own unique characteristics. The episode will also explore the relationship between rational functions and other functions, such as exponential and logarithmic functions.
In addition to graphing, the episode will also cover how to simplify and solve rational functions, including how to find the roots and x-intercepts of a rational function. Viewers will learn how to use polynomial division and synthetic division to simplify a rational function, as well as how to use the quadratic formula to solve for the roots of a rational function.
The episode wraps up with a discussion of how rational functions can be used in real-world applications, such as physics and engineering. Viewers will see how the properties of rational functions can be used to model and analyze complex systems, from the motion of a ball to the flow of a fluid.
Overall, Algebra II season 1 episode 29, "The Algebra of Rational Functions," provides a comprehensive overview of this key algebraic concept. Viewers will learn how to graph, simplify, and solve rational functions, as well as how to apply them to real-world problems. With clear explanations and plenty of examples, this episode is a valuable resource for anyone studying algebra.