Ep 34. Graphing Radical Functions

Algebra I (Beginning Algebra) is a show designed to introduce viewers to the fundamentals of algebra, with a focus on functions, equations, and problem-solving. In season 1 episode 34, entitled Graphing Radical Functions, the show delves into an important topic in algebra: the use of radical functions in graphing.

The episode begins with a brief overview of what radical functions are, and how they differ from other types of functions such as linear or quadratic. Viewers are introduced to the concept of a "radical," which is essentially a fractional exponent. For example, the square root of x can be written as x^(1/2), while the cube root of x can be written as x^(1/3).

The show then moves on to discuss how to graph radical functions. Viewers are shown how to identify the domain and range of a radical function, and how to determine the x- and y-intercepts. The episode also covers how to find and graph vertical and horizontal asymptotes for radical functions.

One of the key challenges in graphing radical functions is dealing with the possibility of negative values under the radical sign. The show explains the concept of "extraneous solutions," which are solutions that arise when you solve an equation but result in a value that is not valid in the original problem. Viewers are shown how to identify and eliminate extraneous solutions when graphing radical functions.

The episode goes on to explore some of the common types of radical functions, such as square root functions and cube root functions. Viewers are shown how to graph these functions using a table of values, and how to identify key features such as the vertex and axis of symmetry.

Throughout the episode, viewers are given plenty of practice problems to work through, both on their own and with the help of the show's host. These problems cover a range of difficulty levels, from simple square root functions to more complex radical expressions involving multiple variables.

Overall, Algebra I (Beginning Algebra) season 1 episode 34, Graphing Radical Functions, provides viewers with a comprehensive introduction to the topic of graphing radical functions. Through clear explanations, helpful examples, and plenty of practice problems, viewers are given the tools they need to understand this important algebraic concept and apply it to their own problem-solving.