Polynomial Functions and Their Graphs

In this lesson, we will learn about polynomial functions and their graphs. We will begin by graphing transformations of monomial functions. A polynomial function such as f(x) = x³ can be used as a basis to easily graph g(x) = (x - 2)³. We can graph f(x) from our knowledge of parent functions and then simply shift all of the points 2 units right to obtain the graph of g(x). Additionally, we will think about the characteristics of the graphs of polynomial functions. We will learn about the end behavior of a polynomial function, which describes what happens to the function as the x-values increase or decrease without bound. We will also learn about the shape of the graph near a zero along with the concept of local maxima and minima. Lastly, we will put everything together and learn how to create a rough sketch of a polynomial function.