This is an important course in polynomial functions. The course module provides an extensive exploration of polynomial functions, focusing on their algebraic identification and graphical analysis. Students will learn to recognize, describe, manipulate, and graph polynomial functions, as well as interpret their key features within mathematical and real-world contexts. This is not limited to defining a polynomial function as a sum of terms with real number coefficients and non-negative integer exponents or distinguishing polynomials from non-polynomial functions. You will learn how other polynomial functions are derived from their respective parents through the process called transformation. This is the main content that defines the shape, size and position orientation of the transformed function.

In the proceeding lectures, an illustration is given that a function graph can change with more than one transformation. This is made possible by using a graphing utility and by using formulas to locate some points on the graph, calculating the turning point(s) and y-intercept. Range and domain of a polynomial function are used to indicate the extent under which a given polynomial function is defined. Examples are given to buttress the points or give more insight into the concept of the areas covered in this course.

Analyzing polynomial function graphs is an in-depth topic in this course that some types of methods (x-intercept, locate principle and turning point) are used in the lectures to achieve such an objective. Interpret the degree and leading coefficient to determine end behavior and maximum number of turning points. In the same study, references to the type of functions (even, odd or neither) are made and how to identify each of them to help us in analyzing the graph of polynomial functions.

The lectures include how to find the real zeros of a polynomial function by using rational root theorem, factor theorem and location principle with the help of synthetic methods. This is important to locate the x-intercept(s) of the function in the graph. The course also includes how to identify the type of polynomial function with its properties to help in interpreting its transformation from its parent function.

We use terminologies like 'open function' and 'closed function' to clearly explain the mechanism of function transformation from its parent function. Other areas like identification, interpretation and graphing polynomial function are covered in this course.

Finally, Sketching accurate graphs of polynomial functions by combining all identified characteristics,

modeling real-world scenarios (example is area calculations) using polynomial functions and using computational tools and resources for further analysis of graphs and properties of polynomial functions are key components of the course.